Metaharmonic lattice point theory. (©2011)

• Record Type: Book
• Further Information: Note: Willi Freeden.
• Other Names: Freeden, W (Willi)
• Contents: Introduction; Historical Aspects; Preparatory Ideas and Concepts; Tasks and Perspectives Basic Notation; Cartesian Nomenclature; Regular Regions; Spherical Nomenclature; Radial and Angular Functions One-Dimensional Auxiliary Material; Gamma Function and Its Properties; Riemann–Lebesgue Limits; Fourier Boundary and Stationary Point Asymptotics; Abel–Poisson and Gauss–Weierstrass Limits One-Dimensional Euler and Poisson Summation Formulas; Lattice Function; Euler Summation Formula for the Laplace Operator; Riemann Zeta Function and Lattice Function; Poisson Summation Formula for the Laplace Operator; Euler Summation Formula for Helmholtz Operators; Poisson Summation Formula for Helmholtz Operators Preparatory Tools of Analytic Theory of Numbers; Lattices in Euclidean Spaces; Basic Results of the Geometry of Numbers; Lattice Points Inside Circles; Lattice Points on Circles; Lattice Points Inside Spheres; Lattice Points on Spheres Preparatory Tools of Mathematical Physics; Integral Theorems for the Laplace Operator; Integral Theorems for the Laplace–Beltrami Operator; Tools Involving the Laplace Operator; Radial and Angular Decomposition of Harmonics; Integral Theorems for the Helmholtz–Beltrami Operator; Radial and Angular Decomposition of Metaharmonics; Tools Involving Helmholtz Operators Preparatory Tools of Fourier Analysis; Periodical Polynomials and Fourier Expansions; Classical Fourier Transform; Poisson Summation and Periodization; Gauss–Weierstrass and Abel–Poisson Transforms; Hankel Transform and Discontinuous Integrals Lattice Function for the Iterated Helmholtz Operator; Lattice Function for the Helmholtz Operator; Lattice Function for the Iterated Helmholtz Operator; Lattice Function in Terms of Circular Harmonics; Lattice Function in Terms of Spherical Harmonics Euler Summation on Regular Regions; Euler Summation Formula for the Iterated Laplace Operator; Lattice Point Discrepancy Involving the Laplace Operator; Zeta Function and Lattice Function; Euler Summation Formulas for Iterated Helmholtz Operators; Lattice Point Discrepancy Involving the Helmholtz Operator Lattice Point Summation; Integral Asymptotics for (Iterated) Lattice Functions; Convergence Criteria and Theorems; Lattice Point-Generated Poisson Summation Formula; Classical Two-Dimensional Hardy–Landau Identity; Multi-Dimensional Hardy–Landau Identities Lattice Ball Summation; Lattice Ball-Generated Euler Summation Formulas; Lattice Ball Discrepancy Involving the Laplacian ; Convergence Criteria and Theorems; Lattice Ball-Generated Poisson Summation Formula; Multi-Dimensional Hardy–Landau Identities Poisson Summation on Regular Regions; Theta Function and Gauss–Weierstrass Summability; Convergence Criteria for the Poisson Series; Generalized Parseval Identity; Minkowski’s Lattice Point Theorem Poisson Summation on Planar Regular Regions; Fourier Inversion Formula; Weighted Two-Dimensional Lattice Point Identities; Weighted Two-Dimensional Lattice Ball Identities Planar Distribution of Lattice Points; Qualitative Hardy–Landau Induced Geometric Interpretation; Constant Weight Discrepancy; Almost Periodicity of the Constant Weight Discrepancy; Angular Weight Discrepancy; Almost Periodicity of the Angular Weight Discrepancy; Radial and Angular Weights; Non-Uniform Distribution of Lattice Points ; Quantitative Step Function Oriented Geometric Interpretation Conclusions; Summary; Outlook Bibliography Index
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2011
• Copyright Date: 2011
• Extent: 1 online resource (xxiv, 448 pages), illustrations
• Subjects: 511.33; Spherical harmonics; Mathematical physics; Spherical functions; Mathematical geography; Earth sciences -- Mathematics; Helmholtz equation; Harmonic functions; Earth sciences -- Mathematics; Harmonic functions; Helmholtz equation; Mathematical geography; Mathematical physics; Spherical functions; Spherical harmonics; Geologi -- Matematik; Talteori; Electronic books
• Languages: English
• ISBNs: 9781439861851; 1439861854
• Related ISBNs: 9781439861844; 1439861846
• Notes: Note: Includes bibliographical references (page 431442) and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.