Willi Freeden

Metaharmonic Lattice Point Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

This work covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. It 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 book presents multi-dimensional techniques for periodization, describes weighted lattice point and ball numbers in georelevant "potato-like" regions, and discusses radial and angular non-uniform lattice point distribution.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 472
• Erscheinungstermin: 9. Mai 2011
• Englisch
• ISBN-13: 9781439861851
• Artikelnr.: 38302239

Autorenporträt

Willi Freeden is the head of the Geomathematics Group in the Department of Mathematics at the University of Kaiserslautern, where he has been vice president for research and technology. Dr. Freeden is also editor-in-chief of the International Journal on Geomathematics. His research interests include special functions of mathematical geophysics, partial differential equations, constructive approximation, numerical methods and scientific computing, and inverse problems in geophysics, geodesy, and satellite technology.

Inhaltsangabe

Introduction. Basic Notation. One-Dimensional Auxiliary Material.
One-Dimensional Euler and Poisson Summation Formulas. Preparatory Tools of
Analytic Theory of Numbers. Preparatory Tools of Mathematical Physics.
Preparatory Tools of Fourier Analysis. Lattice Function for the Iterated
Helmholtz Operator. Euler Summation on Regular Regions. Lattice Point
Summation. Lattice Ball Summation. Poisson Summation on Regular Regions.
Poisson Summation on Planar Regular Regions. Planar Distribution of Lattice
Points. Conclusions. Bibliography. Index.