Transform Methods for Obtaining Asymptotic Expansions of Definite Integrals
With the condition $\int_R {| {dh(t)} |} < \infty $, asymptotic approximations are obtained to the integral $\int_R {f(t)dh(\lambda t)} $ over the real line $R$ as $\lambda \to \infty $, (a) by approximating $\hat h(x)\int_R {e^{ixt} dh(t)} $ in a neighborhood of $x = 0$ and (b) by using a basis...
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| Published in | SIAM journal on mathematical analysis Vol. 3; no. 1; pp. 20 - 30 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.02.1972
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| Subjects | |
| Online Access | Get full text |
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| Abstract | With the condition $\int_R {| {dh(t)} |} < \infty $, asymptotic approximations are obtained to the integral $\int_R {f(t)dh(\lambda t)} $ over the real line $R$ as $\lambda \to \infty $, (a) by approximating $\hat h(x)\int_R {e^{ixt} dh(t)} $ in a neighborhood of $x = 0$ and (b) by using a basis $\{ {\psi _k (t)} \}_{k = 1}^n $, where in contrast to the usual case $\psi _k (t)$ need not be equal to $t^{k - 1} $. |
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| AbstractList | With the condition $\int_R {| {dh(t)} |} < \infty $, asymptotic approximations are obtained to the integral $\int_R {f(t)dh(\lambda t)} $ over the real line $R$ as $\lambda \to \infty $, (a) by approximating $\hat h(x)\int_R {e^{ixt} dh(t)} $ in a neighborhood of $x = 0$ and (b) by using a basis $\{ {\psi _k (t)} \}_{k = 1}^n $, where in contrast to the usual case $\psi _k (t)$ need not be equal to $t^{k - 1} $. |
| Author | Stenger, Frank |
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| CitedBy_id | crossref_primary_10_1137_0504042 crossref_primary_10_1137_1023037 |
| Cites_doi | 10.1007/BF00247684 10.1137/0501036 10.1098/rsta.1969.0039 |
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| Copyright | [Copyright] © 1972 Society for Industrial and Applied Mathematics |
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| DOI | 10.1137/0503003 |
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| References | R2 Romberg W. (R6) 1965; 28 R5 Davis Philip J. (R4) 1967 R8 Rudin Walter (R3) 1962 Titchmarsh E. C. (R7) 1937 |
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| Snippet | With the condition $\int_R {| {dh(t)} |} < \infty $, asymptotic approximations are obtained to the integral $\int_R {f(t)dh(\lambda t)} $ over the real line... |
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| SubjectTerms | Approximation Fourier transforms Integrals Neighborhoods |
| Title | Transform Methods for Obtaining Asymptotic Expansions of Definite Integrals |
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