An Inverse Result of Approximation by Sampling Kantorovich Series
In the present paper, an inverse result of approximation, i.e. a saturation theorem for the sampling Kantorovich operators, is derived in the case of uniform approximation for uniformly continuous and bounded functions on the whole real line. In particular, we prove that the best possible order of a...
Saved in:
| Published in | Proceedings of the Edinburgh Mathematical Society Vol. 62; no. 1; pp. 265 - 280 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.02.2019
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | In the present paper, an inverse result of approximation, i.e. a saturation theorem for the sampling Kantorovich operators, is derived in the case of uniform approximation for uniformly continuous and bounded functions on the whole real line. In particular, we prove that the best possible order of approximation that can be achieved by the above sampling series is the order one, otherwise the function being approximated turns out to be a constant. The above result is proved by exploiting a suitable representation formula which relates the sampling Kantorovich series with the well-known generalized sampling operators introduced by Butzer. At the end, some other applications of such representation formulas are presented, together with a discussion concerning the kernels of the above operators for which such an inverse result occurs. |
|---|---|
| AbstractList | In the present paper, an inverse result of approximation, i.e. a saturation theorem for the sampling Kantorovich operators, is derived in the case of uniform approximation for uniformly continuous and bounded functions on the whole real line. In particular, we prove that the best possible order of approximation that can be achieved by the above sampling series is the order one, otherwise the function being approximated turns out to be a constant. The above result is proved by exploiting a suitable representation formula which relates the sampling Kantorovich series with the well-known generalized sampling operators introduced by Butzer. At the end, some other applications of such representation formulas are presented, together with a discussion concerning the kernels of the above operators for which such an inverse result occurs. |
| Author | Costarelli, Danilo Vinti, Gianluca |
| Author_xml | – sequence: 1 givenname: Danilo orcidid: 0000-0001-8834-8877 surname: Costarelli fullname: Costarelli, Danilo email: danilo.costarelli@unipg.it organization: Department of Mathematics and Computer Science, University of Perugia, 1 Via Vanvitelli, 06123 Perugia, Italy (danilo.costarelli@unipg.it; gianluca.vinti@unipg.it) – sequence: 2 givenname: Gianluca surname: Vinti fullname: Vinti, Gianluca email: danilo.costarelli@unipg.it organization: Department of Mathematics and Computer Science, University of Perugia, 1 Via Vanvitelli, 06123 Perugia, Italy (danilo.costarelli@unipg.it; gianluca.vinti@unipg.it) |
| BookMark | eNp9kE9LAzEQxYNUsK1-AG8Bz6uZZHezPZbin2JBsHpestNsTdkma7It9tub2oKg6GkO834z770B6VlnNSGXwK6BgbyZMwaCjSCDgjEmUn5C-pDmaSIKMeqR_n6d7PdnZBDCKmqkzKBPxmNLp3arfdD0WYdN01FX03Hbevdh1qozztJqR-dq3TbGLumjsp3zbmvwjc61Nzqck9NaNUFfHOeQvN7dvkwektnT_XQyniUoctYlesEVokJV6UxXOUpZI6-URpCcKZmpVBZQ1RitZxJHC84qzDnwGjKUoFEMydXhbrT2vtGhK1du4218WfKYnAsBBUSVPKjQuxC8rks03VeMzivTlMDKfV_lr74iCT_I1scG_O5fRhwZta68WSz1t6m_qU-o431h |
| CitedBy_id | crossref_primary_10_1007_s00025_019_1044_5 crossref_primary_10_1007_s00025_021_01520_4 crossref_primary_10_1016_j_amc_2022_127152 crossref_primary_10_1007_s13398_020_00936_x crossref_primary_10_1515_ans_2022_0023 crossref_primary_10_1016_j_amc_2019_124623 crossref_primary_10_1007_s40574_020_00256_3 crossref_primary_10_33205_cma_876890 crossref_primary_10_1016_j_fss_2025_109332 crossref_primary_10_1142_S0219530519500155 crossref_primary_10_1007_s13398_022_01367_6 crossref_primary_10_1007_s13398_024_01571_6 crossref_primary_10_3390_math7030259 crossref_primary_10_1002_mma_10330 crossref_primary_10_1002_mma_7420 crossref_primary_10_1007_s43037_020_00071_0 crossref_primary_10_1002_mma_9202 crossref_primary_10_1007_s13398_020_00805_7 crossref_primary_10_1515_dema_2022_0014 crossref_primary_10_1007_s13398_023_01535_2 crossref_primary_10_1016_j_amc_2020_125046 crossref_primary_10_1016_j_jat_2019_03_001 crossref_primary_10_1007_s41980_024_00868_x crossref_primary_10_1007_s00025_021_01383_9 crossref_primary_10_1016_j_cagd_2021_102062 crossref_primary_10_33205_cma_484500 crossref_primary_10_3390_app13095594 crossref_primary_10_1016_j_eswa_2023_122350 crossref_primary_10_1007_s13398_024_01605_z crossref_primary_10_3390_sym13081450 crossref_primary_10_3934_mfc_2021031 crossref_primary_10_1016_j_fss_2021_03_003 crossref_primary_10_1016_j_jmaa_2023_127740 crossref_primary_10_1007_s12215_020_00544_z crossref_primary_10_1016_j_amc_2019_02_076 crossref_primary_10_1007_s13324_019_00334_6 crossref_primary_10_1016_j_avsg_2019_05_002 crossref_primary_10_1016_j_jmaa_2021_125913 crossref_primary_10_1007_s00009_019_1315_0 crossref_primary_10_1007_s00009_023_02459_2 crossref_primary_10_1007_s00521_018_03998_6 crossref_primary_10_3390_axioms12121124 crossref_primary_10_1007_s00025_020_01241_0 crossref_primary_10_1002_mma_5838 crossref_primary_10_1007_s00041_022_09943_5 crossref_primary_10_1002_mana_202100117 |
| Cites_doi | 10.1216/JIE-2014-26-4-455 10.1007/978-3-319-34189-7 10.1002/sapm1969483265 10.1007/BF03549524 10.1016/j.amc.2017.08.058 10.1016/j.jat.2016.05.001 10.1016/j.cagd.2012.07.005 10.1016/0021-9045(70)90058-4 10.1016/j.jat.2015.10.001 10.1007/BF03549462 10.1016/j.jat.2014.06.004 10.1080/01630563.2013.767833 10.1016/j.cagd.2012.03.011 10.1080/01630563.2015.1040888 10.1007/s11075-010-9418-5 10.1016/j.ndteint.2014.10.001 10.1007/BF03549509 10.1007/BF03549542 10.1080/01630563.2011.652270 10.1007/s00025-016-0546-7 10.1109/TIT.2009.2034793 10.1016/0021-9991(85)90006-3 10.1016/j.jmaa.2017.01.066 10.1016/0771-050X(81)90008-5 10.1016/j.cam.2012.02.028 10.1007/s10114-011-0227-0 10.1007/BF03549552 10.1007/978-0-387-70914-7 10.1007/978-3-0348-7448-9 10.1109/TSP.2007.914346 10.1093/oso/9780198596998.001.0001 10.1002/pamm.200810937 10.1216/JIE-2014-26-3-345 10.1080/00036811.2010.499506 10.1080/00036811.2012.698267 |
| ContentType | Journal Article |
| Copyright | Copyright © Edinburgh Mathematical Society 2018 |
| Copyright_xml | – notice: Copyright © Edinburgh Mathematical Society 2018 |
| DBID | AAYXX CITATION 3V. 7SC 7XB 88I 8AL 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- L6V L7M L~C L~D M0N M2P M7S P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U |
| DOI | 10.1017/S0013091518000342 |
| DatabaseTitle | CrossRef Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection ProQuest Computing Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection ProQuest One Academic ProQuest Central (Alumni) ProQuest One Academic (New) |
| DatabaseTitleList | Computer Science Database CrossRef |
| Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| DocumentTitleAlternate | D. Costarelli and G. Vinti An inverse result of approximation by Sw |
| EISSN | 1464-3839 |
| EndPage | 280 |
| ExternalDocumentID | 10_1017_S0013091518000342 |
| GroupedDBID | -1D -1F -2P -2V -E. -~6 -~N -~X .FH 09C 09E 0E1 0R~ 123 29O 3V. 4.4 5VS 6OB 6~7 74X 74Y 7~V 88I 8FE 8FG 8R4 8R5 9M5 AAAZR AABES AABWE AACJH AAEED AAGFV AAKTX AAMNQ AANRG AARAB AASVR AAUIS AAUKB ABBXD ABBZL ABEFU ABITZ ABJCF ABJNI ABKKG ABMWE ABMYL ABQTM ABQWD ABROB ABTAH ABTCQ ABUWG ABVFV ABXAU ABZCX ABZUI ACBMC ACCHT ACETC ACGFS ACGOD ACIMK ACIPV ACIWK ACMRT ACNCT ACQFJ ACREK ACUIJ ACUYZ ACWGA ACYZP ACZBM ACZUX ACZWT ADCGK ADDNB ADFEC ADGEJ ADKIL ADOCW ADOJD ADOVH ADOVT ADVJH AEBAK AEBPU AEHGV AEMTW AENCP AENEX AENGE AEYYC AFFNX AFFUJ AFKQG AFKRA AFKSM AFLOS AFLVW AFUTZ AGABE AGBYD AGJUD AGLWM AGOOT AHQXX AHRGI AIGNW AIHIV AIOIP AISIE AJ7 AJCYY AJPFC AJQAS AKZCZ ALMA_UNASSIGNED_HOLDINGS ALVPG ALWZO AQJOH ARABE ARAPS ARZZG ATUCA AUXHV AYIQA AZQEC BBLKV BCGOX BENPR BESQT BGHMG BGLVJ BJBOZ BLZWO BMAJL BPHCQ BQFHP C0O CAG CBIIA CCPQU CCQAD CCUQV CDIZJ CFAFE CFBFF CGQII CHEAL CJCSC COF CS3 DC4 DOHLZ DU5 DWQXO EBS EGQIC EJD FRP GNUQQ HCIFZ HG- HST HZ~ H~9 I.6 I.7 I.9 IH6 IOEEP IOO IS6 I~P J36 J38 J3A JHPGK JQKCU K6V K7- KAFGG KC5 KCGVB KFECR L6V L98 LHUNA LW7 M-V M0N M2P M7S M7~ M8. NIKVX NMFBF NZEOI O9- OHT OK1 OYBOY P2P P62 PQQKQ PROAC PTHSS PYCCK Q2X RAMDC RCA RIG RNI ROL RR0 RZO S6- S6U SAAAG T9M TR2 TWZ UT1 WFFJZ WH7 WQ3 WXU WXY WYP XOL YNT ZCG ZDLDU ZJOSE ZMEZD ZY4 ZYDXJ ~V1 AAKNA AATMM AAYXX ABGDZ ABHFL ABVKB ABVZP ABXHF ACDLN ACEJA ACOZI ACRPL ADNMO AEMFK AFZFC AGQPQ AHDLI AKMAY AMVHM ANOYL CITATION PHGZM PHGZT 7SC 7XB 8AL 8FD 8FK JQ2 L7M L~C L~D PKEHL PQEST PQGLB PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c360t-ed2accacabe5eb6c77fc2baec1720a75a4781bfc34257c9d20bc6212f15c71ec3 |
| IEDL.DBID | BENPR |
| ISSN | 0013-0915 |
| IngestDate | Fri Jul 25 19:36:01 EDT 2025 Tue Jul 01 03:48:13 EDT 2025 Thu Apr 24 23:02:06 EDT 2025 Wed Mar 13 05:47:42 EDT 2024 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | saturation theorem central B-splines sampling Kantorovich series 41A30 order of approximation 47A58 generalized sampling operators inverse results Primary 41A25 41A05 |
| Language | English |
| License | https://www.cambridge.org/core/terms |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c360t-ed2accacabe5eb6c77fc2baec1720a75a4781bfc34257c9d20bc6212f15c71ec3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-8834-8877 |
| OpenAccessLink | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/0974FFC764B0E44E9261C1704352E828/S0013091518000342a.pdf/div-class-title-an-inverse-result-of-approximation-by-sampling-kantorovich-series-div.pdf |
| PQID | 2309233181 |
| PQPubID | 41713 |
| PageCount | 16 |
| ParticipantIDs | proquest_journals_2309233181 crossref_citationtrail_10_1017_S0013091518000342 crossref_primary_10_1017_S0013091518000342 cambridge_journals_10_1017_S0013091518000342 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 20190200 2019-02-00 20190201 |
| PublicationDateYYYYMMDD | 2019-02-01 |
| PublicationDate_xml | – month: 02 year: 2019 text: 20190200 |
| PublicationDecade | 2010 |
| PublicationPlace | Cambridge, UK |
| PublicationPlace_xml | – name: Cambridge, UK – name: Cambridge |
| PublicationTitle | Proceedings of the Edinburgh Mathematical Society |
| PublicationTitleAlternate | Proceedings of the Edinburgh Mathematical Society |
| PublicationYear | 2019 |
| Publisher | Cambridge University Press |
| Publisher_xml | – name: Cambridge University Press |
| References | S0013091518000342_ref37 S0013091518000342_ref8 S0013091518000342_ref9 S0013091518000342_ref35 S0013091518000342_ref7 S0013091518000342_ref14 S0013091518000342_ref36 S0013091518000342_ref39 S0013091518000342_ref18 Costarelli (S0013091518000342_ref19) 2011; 9 Coroianu (S0013091518000342_ref17) 2012; 11 S0013091518000342_ref4 Coroianu (S0013091518000342_ref15) 2010; 9 S0013091518000342_ref5 Bardaro (S0013091518000342_ref6) 2007; 6 Unser (S0013091518000342_ref42) 1997 S0013091518000342_ref40 S0013091518000342_ref41 Asdrubali (S0013091518000342_ref2) 2018; 317 S0013091518000342_ref22 S0013091518000342_ref23 Coroianu (S0013091518000342_ref16) 2011; 10 S0013091518000342_ref20 S0013091518000342_ref21 S0013091518000342_ref26 S0013091518000342_ref24 S0013091518000342_ref25 Kivinukk (S0013091518000342_ref31) 2009; 8 S0013091518000342_ref28 S0013091518000342_ref29 Wang (S0013091518000342_ref44) 2013; 92 Bardaro (S0013091518000342_ref3) 2010; 62 Higgins (S0013091518000342_ref30) 1996 Ries (S0013091518000342_ref38) 1984 Butzer (S0013091518000342_ref12) 1993 Alavi (S0013091518000342_ref1) 2013; 2013 Cluni (S0013091518000342_ref13) 2015; 19 Vinti (S0013091518000342_ref43) 2017 S0013091518000342_ref11 S0013091518000342_ref33 Do (S0013091518000342_ref27) 2008; 56 S0013091518000342_ref34 S0013091518000342_ref10 S0013091518000342_ref32 |
| References_xml | – ident: S0013091518000342_ref22 doi: 10.1216/JIE-2014-26-4-455 – ident: S0013091518000342_ref9 doi: 10.1007/978-3-319-34189-7 – ident: S0013091518000342_ref28 doi: 10.1002/sapm1969483265 – volume: 9 start-page: 59 year: 2010 ident: S0013091518000342_ref15 article-title: Approximation by nonlinear generalized sampling operators of max-product kind publication-title: Sampl. Theory Signal Image Process. doi: 10.1007/BF03549524 – volume: 317 start-page: 160 year: 2018 ident: S0013091518000342_ref2 article-title: Detection of thermal bridges from thermographic images by means of image processing approximation algorithms publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2017.08.058 – ident: S0013091518000342_ref25 doi: 10.1016/j.jat.2016.05.001 – ident: S0013091518000342_ref39 doi: 10.1016/j.cagd.2012.07.005 – volume: 19 start-page: 602 year: 2015 ident: S0013091518000342_ref13 article-title: Applications of sampling Kantorovich operators to thermographic images for seismic engineering publication-title: J. Comput. Anal. Appl. – ident: S0013091518000342_ref34 doi: 10.1016/0021-9045(70)90058-4 – ident: S0013091518000342_ref37 doi: 10.1016/j.jat.2015.10.001 – volume: 6 start-page: 29 year: 2007 ident: S0013091518000342_ref6 article-title: Kantorovich-type generalized sampling series in the setting of Orlicz spaces publication-title: Sampl. Theory Signal Image Process. doi: 10.1007/BF03549462 – start-page: 157 volume-title: Linear prediction by samples from the past year: 1993 ident: S0013091518000342_ref12 – start-page: 422 volume-title: Ten good reasons for using spline wavelets year: 1997 ident: S0013091518000342_ref42 – volume: 62 start-page: 247 year: 2010 ident: S0013091518000342_ref3 article-title: Voronovskaja formulae for Kantorovich generalized sampling series publication-title: Int. J. Pure Appl. Math – ident: S0013091518000342_ref18 doi: 10.1016/j.jat.2014.06.004 – ident: S0013091518000342_ref20 doi: 10.1080/01630563.2013.767833 – volume: 9 start-page: 445 year: 2011 ident: S0013091518000342_ref19 publication-title: Boll. Unione Mat. Ital. – ident: S0013091518000342_ref33 doi: 10.1016/j.cagd.2012.03.011 – ident: S0013091518000342_ref23 doi: 10.1080/01630563.2015.1040888 – ident: S0013091518000342_ref41 doi: 10.1007/s11075-010-9418-5 – ident: S0013091518000342_ref14 doi: 10.1016/j.ndteint.2014.10.001 – volume: 8 start-page: 77 year: 2009 ident: S0013091518000342_ref31 article-title: Interpolating generalized Shannon sampling operators, their norms and approximation properties publication-title: Sampl. Theory Signal Image Process. doi: 10.1007/BF03549509 – volume: 10 start-page: 211 year: 2011 ident: S0013091518000342_ref16 article-title: Approximation by max-product sampling operators based on sinc-type kernels publication-title: Sampl. Theory Signal Image Process. doi: 10.1007/BF03549542 – ident: S0013091518000342_ref5 doi: 10.1080/01630563.2011.652270 – ident: S0013091518000342_ref24 doi: 10.1007/s00025-016-0546-7 – ident: S0013091518000342_ref7 doi: 10.1109/TIT.2009.2034793 – ident: S0013091518000342_ref35 doi: 10.1016/0021-9991(85)90006-3 – year: 2017 ident: S0013091518000342_ref43 article-title: A general approximation approach for the simultaneous treatment of integral and discrete operators publication-title: Adv. Nonlinear Stud. – ident: S0013091518000342_ref26 doi: 10.1016/j.jmaa.2017.01.066 – ident: S0013091518000342_ref36 doi: 10.1016/0771-050X(81)90008-5 – ident: S0013091518000342_ref29 doi: 10.1016/j.cam.2012.02.028 – ident: S0013091518000342_ref4 doi: 10.1007/s10114-011-0227-0 – volume: 11 start-page: 113 year: 2012 ident: S0013091518000342_ref17 article-title: Saturation results for the truncated max-product sampling operators based on sinc and Fejér-type kernels publication-title: Sampl. Theory Signal Image Process. doi: 10.1007/BF03549552 – volume: 2013 year: 2013 ident: S0013091518000342_ref1 article-title: Applying cubic B-Spline quasi-interpolation to solve 1D wave equations in polar coordinates publication-title: ISRN Comput. Math. – ident: S0013091518000342_ref10 doi: 10.1007/978-0-387-70914-7 – ident: S0013091518000342_ref11 doi: 10.1007/978-3-0348-7448-9 – start-page: 746 volume-title: Approximation by generalized sampling series year: 1984 ident: S0013091518000342_ref38 – volume: 56 start-page: 2334 year: 2008 ident: S0013091518000342_ref27 article-title: A theory for sampling signals from a union of subspaces publication-title: IEEE Trans. Signal. Process. doi: 10.1109/TSP.2007.914346 – volume-title: Sampling theory in Fourier and signal analysis: foundations year: 1996 ident: S0013091518000342_ref30 doi: 10.1093/oso/9780198596998.001.0001 – ident: S0013091518000342_ref40 doi: 10.1002/pamm.200810937 – ident: S0013091518000342_ref21 doi: 10.1216/JIE-2014-26-3-345 – ident: S0013091518000342_ref8 doi: 10.1080/00036811.2010.499506 – ident: S0013091518000342_ref32 – volume: 92 start-page: 1682 year: 2013 ident: S0013091518000342_ref44 article-title: A numerical method for solving KdV equation with multilevel B-spline quasi-interpolation publication-title: Appl. Anal. doi: 10.1080/00036811.2012.698267 |
| SSID | ssj0007751 |
| Score | 2.3770306 |
| Snippet | In the present paper, an inverse result of approximation, i.e. a saturation theorem for the sampling Kantorovich operators, is derived in the case of uniform... |
| SourceID | proquest crossref cambridge |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 265 |
| SubjectTerms | Approximation Continuity (mathematics) Mathematical analysis Operators (mathematics) Representations Sampling |
| Title | An Inverse Result of Approximation by Sampling Kantorovich Series |
| URI | https://www.cambridge.org/core/product/identifier/S0013091518000342/type/journal_article https://www.proquest.com/docview/2309233181 |
| Volume | 62 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LSwMxEA62vehBfGK1lhw8iYv7aJLdk6zSWpQWqRZ6K8kkq0LZ1u4W9N-b7KsWodfNBpbJ7Jcvk5lvELpSKuLE5rYFVHiWRj9qBdIjGgw5D5Q-Y3gdU-A8GNL-uPM0IZMi4JYUaZUlJmZALedgYuS3miprLqI90LlbfFmma5S5XS1aaNRQQ0Owrw9fjfvu8GVUYTFjxKl6GAQOKe81M9Foc2mnnzl-ptLi_lVX2NylNkE623l6B2i_oIw4zNf4EO2o-AjtDSq91eQYhWGMjWLGMlF4pJLVLMXzCIdGL_z7My9OxOIHv3KTPx6_42fTOtgEE-ADm_iYSk7QuNd9e-hbRXMECzxqp5aSLtfWBy4UUYICYxG4givQjMTmjHBTQyoi8MxPCYF0bQFUGylyCDBHgXeK6vE8VmcIB75NhK1HfAUdNwo4EClpIBlIKknEmuimMsy0cPFkmqeHsek_OzaRXdpuCoXQuOl3Mds25bqasshVNra93CoXZP01a_c43z58gXY15wnyxOsWqqfLlbrUvCIVbVTze4_twoV-ATbzx9k |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV07T8MwED4VGIAB8RTl6QEWREQedVwPCFVAKZR2gCKxBfvsABJKgRRB_xS_ETtpAgipG2scW9b5893ZvvsOYEfrWFBXuA6GMnCM9gsdrgJqlKEQXJszRlCzCc6dbti6qV3c0tsKfBa5MDasstCJmaJWfbR35AfGVTa-iEGgd_T84tiqUfZ1tSihkcOirYfv5siWHp6fmPXd9f3mae-45YyqCjgYhO7A0coXZtoopKZahshYjL4UGo0pdwWjwiZfyhgDi2bkynclhkbBxx5F5mkMzLgTMFULAm53VL15Vmp-xqhXVkzgHi1eUTOKavtEaL559YwTxv_J5fDbJv42CZmda87D3MhBJY0cUQtQ0ckizHZKdtd0CRqNhFh-jtdUkyudvj0NSD8mDctO_vGYp0ISOSTXwkarJ_ekbQsV26sLfCD2Nk6ny3DzL0Jbgcmkn-hVILzuUumalrrGmh9zgVSpkCuGKlQ0ZlXYLwUTjTZUGuXBaCz6I8cquIXsIhzRmtvqGk_juuyVXZ5zTo9xP28UC_I9m28wro1v3obpVq9zGV2ed9vrMGO8LZ6HfG_A5OD1TW8aj2YgtzIYEbj7b9x-ARnyBQA |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+Inverse+Result+of+Approximation+by+Sampling+Kantorovich+Series&rft.jtitle=Proceedings+of+the+Edinburgh+Mathematical+Society&rft.au=Costarelli%2C+Danilo&rft.au=Vinti%2C+Gianluca&rft.date=2019-02-01&rft.pub=Cambridge+University+Press&rft.issn=0013-0915&rft.eissn=1464-3839&rft.volume=62&rft.issue=1&rft.spage=265&rft.epage=280&rft_id=info:doi/10.1017%2FS0013091518000342 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0013-0915&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0013-0915&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0013-0915&client=summon |