Local Convergence of the Continuous and Semi-Discrete Wavelet Transform in Lp(R)

The smoothness of functions f in the space Lp(R) with 1<p<∞ is studied through the local convergence of the continuous wavelet transform of f. Additionally, we study the smoothness of functions in Lp(R) by means of the local convergence of the semi-discrete wavelet transform.

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Published inMathematics (Basel) Vol. 9; no. 5; p. 522
Main Authors Navarro-Fuentes, Jaime, Arellano-Balderas, Salvador, Herrera-Alcántara, Oscar
Format Journal Article
LanguageEnglish
Published 03.03.2021
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Abstract The smoothness of functions f in the space Lp(R) with 1<p<∞ is studied through the local convergence of the continuous wavelet transform of f. Additionally, we study the smoothness of functions in Lp(R) by means of the local convergence of the semi-discrete wavelet transform.
AbstractList The smoothness of functions f in the space Lp(R) with 1<p<∞ is studied through the local convergence of the continuous wavelet transform of f. Additionally, we study the smoothness of functions in Lp(R) by means of the local convergence of the semi-discrete wavelet transform.
Author Herrera-Alcántara, Oscar
Navarro-Fuentes, Jaime
Arellano-Balderas, Salvador
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10.1007/s00041-009-9109-6
10.1021/ci010333v
10.1142/S0219691311004262
10.1016/j.chemolab.2003.08.001
10.1142/S0218202596000262
10.1016/S0893-6080(05)80129-7
10.1007/s43036-019-00010-3
10.2748/tmj/1113246676
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References Rao (ref_13) 1994; 23
Firdous (ref_16) 2012; 127
Ashurov (ref_3) 2011; 24
ref_11
Wilson (ref_5) 2010; 16
Xueguang (ref_15) 2003; 69
Navarro (ref_21) 2020; 24
ref_19
Navarro (ref_20) 2019; 32
Minai (ref_23) 1993; 6
ref_18
Pathak (ref_9) 2004; 56
Perrier (ref_10) 1996; 6
Kaiser (ref_12) 2008; 186
Navarro (ref_1) 2012; 5
ref_25
Abdesselem (ref_17) 2016; 96
ref_24
Li (ref_7) 2012; 18
Navarro (ref_2) 2020; 5
Nie (ref_14) 2002; 42
Weisz (ref_6) 2013; 138
Sunmonu (ref_22) 2017; 5
ref_26
ref_4
Ashurov (ref_8) 2011; 9
References_xml – volume: 23
  start-page: 761
  year: 1994
  ident: ref_13
  article-title: Application of Carleson’s Theorem to wavelet inversion
  publication-title: Control Cybern.
  contributor:
    fullname: Rao
– ident: ref_24
– ident: ref_26
– volume: 138
  start-page: 237
  year: 2013
  ident: ref_6
  article-title: Inversion formula for the continuous wavelet transform
  publication-title: Acta Math. Hungar.
  doi: 10.1007/s10474-012-0263-y
  contributor:
    fullname: Weisz
– volume: 5
  start-page: 2
  year: 2017
  ident: ref_22
  article-title: Wavelet neural network model for yield spread forecasting
  publication-title: Mathematics
  contributor:
    fullname: Sunmonu
– volume: 127
  start-page: 6311
  year: 2012
  ident: ref_16
  article-title: Implementation of wavelet solutions to second order differential equations with Maple
  publication-title: Appl. Math. Sci.
  contributor:
    fullname: Firdous
– volume: 96
  start-page: 418
  year: 2016
  ident: ref_17
  article-title: Wavelet neural networks for DNA sequence classification using the genetic algorithms and the Least Trimmed Square
  publication-title: Proc. Comp. Sci.
  doi: 10.1016/j.procs.2016.08.088
  contributor:
    fullname: Abdesselem
– ident: ref_11
  doi: 10.1137/1.9781611970104
– volume: 18
  start-page: 439
  year: 2012
  ident: ref_7
  article-title: Pointwise convergence of the Calderon reproducing formula
  publication-title: J. Fourier Anal.
  doi: 10.1007/s00041-011-9211-4
  contributor:
    fullname: Li
– volume: 24
  start-page: 1578
  year: 2011
  ident: ref_3
  article-title: On continuous wavelet transform of distributions
  publication-title: Appl. Math. Lett.
  doi: 10.1016/j.aml.2011.03.050
  contributor:
    fullname: Ashurov
– volume: 186
  start-page: 101
  year: 2008
  ident: ref_12
  article-title: Wavelet transform for functions with values in UMD spaces
  publication-title: Stud. Math.
  doi: 10.4064/sm186-2-1
  contributor:
    fullname: Kaiser
– ident: ref_18
  doi: 10.1109/IPTA.2008.4743756
– volume: 16
  start-page: 768
  year: 2010
  ident: ref_5
  article-title: How fast and in what sense does the Calderon reproducing formula converge?
  publication-title: J. Fourier Anal. Appl.
  doi: 10.1007/s00041-009-9109-6
  contributor:
    fullname: Wilson
– ident: ref_25
– ident: ref_4
– volume: 42
  start-page: 274
  year: 2002
  ident: ref_14
  article-title: Approximate derivative calculated by using continuous wavelet transform
  publication-title: J. Chem. Inf. Comp. Sci.
  doi: 10.1021/ci010333v
  contributor:
    fullname: Nie
– volume: 32
  start-page: 166
  year: 2019
  ident: ref_20
  article-title: Smothness of wek solutions under lineal partial differential operators with constant coefficients via the convergence of the n-dimensional continuous shearlet transform
  publication-title: Int. Trans. Spec. Funct.
  contributor:
    fullname: Navarro
– volume: 9
  start-page: 675
  year: 2011
  ident: ref_8
  article-title: Convergence of the continuous wavelet transform on the entire Lebesgue set of Lp functions
  publication-title: Int. J. Wavelets Multiresolut. Inf.
  doi: 10.1142/S0219691311004262
  contributor:
    fullname: Ashurov
– volume: 69
  start-page: 157
  year: 2003
  ident: ref_15
  article-title: A general approach to derivative calculation using wavelet transform
  publication-title: Chem. Int. Lab. Syst.
  doi: 10.1016/j.chemolab.2003.08.001
  contributor:
    fullname: Xueguang
– volume: 24
  start-page: 469
  year: 2020
  ident: ref_21
  article-title: Fast Convergence of the Two Dimensional Discrete Shearlet Transform
  publication-title: Comp. Sist.
  contributor:
    fullname: Navarro
– volume: 6
  start-page: 649
  year: 1996
  ident: ref_10
  article-title: Besov norm in terms of the continuous wavelet transform. Applications to structure functions
  publication-title: Math. Models Methods Appl. Sci.
  doi: 10.1142/S0218202596000262
  contributor:
    fullname: Perrier
– volume: 6
  start-page: 845
  year: 1993
  ident: ref_23
  article-title: On the Derivatives of the Sigmoid
  publication-title: Neural Netw.
  doi: 10.1016/S0893-6080(05)80129-7
  contributor:
    fullname: Minai
– volume: 5
  start-page: 143
  year: 2020
  ident: ref_2
  article-title: Convergence of the continuous wavelet transform with rotations in higher dimensions
  publication-title: Adv. Oper. Theory
  doi: 10.1007/s43036-019-00010-3
  contributor:
    fullname: Navarro
– volume: 5
  start-page: 95
  year: 2012
  ident: ref_1
  article-title: The one dimensional regularity of the continuous wavelet transform applied to weak solutions
  publication-title: Pioneer J. Math. Math. Sci.
  contributor:
    fullname: Navarro
– ident: ref_19
– volume: 56
  start-page: 411
  year: 2004
  ident: ref_9
  article-title: The wavelet transform of distributions
  publication-title: Tohoku Math. J.
  doi: 10.2748/tmj/1113246676
  contributor:
    fullname: Pathak
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