Freeden, Willi Metaharmonic Lattice Point Theory 9781138382107

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Автор: Freeden, Willi
Название: Metaharmonic Lattice Point Theory
ISBN: 9781138382107
Издательство: Taylor&Francis
Классификация:

Прикладная математика

Геофизика

Науки о земле

Экология, охрана окружающей среды, экологичные технологии

Сельскохозяйственная наука

ISBN-10: 1138382108
Обложка/Формат: Paperback
Страницы: 476
Вес: 0.88 кг.
Дата издания: 30.08.2019
Серия: Chapman & Hall Pure and Applied Mathematics
Язык: English
Иллюстрации: 3 tables, black and white; 35 illustrations, black and white
Размер: 235 x 159
Читательская аудитория: Tertiary education (us: college)
Основная тема: Geophysics
Ссылка на Издательство: Link
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Поставляется из: Европейский союз
Описание:

Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. The book establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of weighted lattice point numbers, in particular the non-uniform distribution of lattice points.

The author explains how to obtain multi-dimensional generalizations of the Euler summation formula by interpreting classical Bernoulli polynomials as Greens functions and linking them to Zeta and Theta functions. To generate multi-dimensional Euler summation formulas on arbitrary lattices, the Helmholtz wave equation must be converted into an associated integral equation using Greens functions as bridging tools. After doing this, the weighted sums of functional values for a prescribed system of lattice points can be compared with the corresponding integral over the function.

Exploring special function systems of Laplace and Helmholtz equations, this book focuses on the analytic theory of numbers in Euclidean spaces based on methods and procedures of mathematical physics. It shows how these fundamental techniques are used in geomathematical research areas, including gravitation, magnetics, and geothermal.

Metaharmonic Lattice Point Theory, Freeden, Willi