Lattice point identities and Shannon-type sampling
This book leads the reader through a research excursion, beginning from the Gaussian circle problem of the early nineteenth century, via the classical Hardy-Landau lattice point identity and the Hardy conjecture of the first half of the twentieth century, and the Shannon sampling theorem (its varian...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
London :
CRC Press LLC,
2019.
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| Series: | Chapman and Hall/CRC Monographs and Research Notes in Mathematics Ser.
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| Subjects: | |
| Online Access: | Taylor & Francis OCLC metadata license agreement |
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Add Tag | Summary: | This book leads the reader through a research excursion, beginning from the Gaussian circle problem of the early nineteenth century, via the classical Hardy-Landau lattice point identity and the Hardy conjecture of the first half of the twentieth century, and the Shannon sampling theorem (its variants, generalizations and the fascinating stories about the cardinal series) of the second half of the twentieth century. The authors demonstrate how all these facets have resulted in new multivariate extensions of lattice point identities and Shannon-type sampling procedures of high practical applicability, thereby also providing a general reproducing kernel Hilbert space structure of an associated Paley-Wiener theory over (potato-like) bounded regions (cf. the cover illustration of the geoid), as well as the whole Euclidean space. |
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| Item Description: | Description based upon print version of record. 10.1 Integral Mean Asymptotics for the Euler-Green Function |
| Physical Description: | 1 online resource (325 pages). |
| ISBN: | 9781000756524 1000756521 9780429355103 0429355106 9781000757743 1000757749 |
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