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Books > Professional & Technical > Energy technology & engineering > Electrical engineering
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Lattice Point Identities and Shannon-Type Sampling (Hardcover)
Loot Price: R4,793
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Lattice Point Identities and Shannon-Type Sampling (Hardcover)
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Expected to ship within 12 - 19 working days
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Lattice Point Identities and Shannon-Type Sampling demonstrates
that significant roots of many recent facets of Shannon's sampling
theorem for multivariate signals rest on basic number-theoretic
results. 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. All in all, the context of this book represents the fruits
of cross-fertilization of various subjects, namely elliptic partial
differential equations, Fourier inversion theory, constructive
approximation involving Euler and Poisson summation formulas,
inverse problems reflecting the multivariate antenna problem, and
aspects of analytic and geometric number theory. Features: New
convergence criteria for alternating series in multi-dimensional
analysis Self-contained development of lattice point identities of
analytic number theory Innovative lattice point approach to Shannon
sampling theory Useful for students of multivariate constructive
approximation, and indeed anyone interested in the applicability of
signal processing to inverse problems.
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