Lattice point identities and Shannon-type sampling. ([2020])

• Record Type: Book
• Further Information: Note: Willi Freeden, M. Zuhair Nashed.
• Authors: Freeden, W (Willi); Nashed, M. Zuhair
• Contents: Cover; Half Title; Series Page; Title Page; Copyright Page; Contents; Preface; Authors; Acknowledgments; Part I: Central Theme; 1. From Lattice Point to Shannon-Type Sampling Identities; 1.1 Classical Framework of Shannon Sampling; 1.2 Transition From Shannon to Shannon-Type Sampling; 1.3 Novel Framework of Shannon-Type Sampling; 2. Obligations, Ingredients, Achievements, and Innovations; 2.1 Obligations and Ingredients; 2.2 Achievements and Innovative Results; 2.3 Methods and Tools; 3. Layout; 3.1 Structural Organisation; 3.2 Relationship to Other Monographs Part II: Univariate Poisson-Type Summation Formulas and Shannon-Type Sampling4. Euler/Poisson-Type Summation Formulas and Shannon-Type Sampling; 4.1 Classical Euler Summation Formula; 4.2 Variants of the Euler Summation Formula; 4.3 Poisson-Type Summation Formula over Finite Intervals; 4.4 Shannon Sampling Based on the Poisson Summation-Type Formula; 4.5 Shannon-Type Sampling Based on Poisson Summation-Type Formulas; 4.6 Fourier Transformed Values-Based Shannon-Type Sampling (Finite Intervals); 4.7 Functional Values-Based Shannon-Type Sampling (Finite Intervals) 4.8 Paley-Wiener Reproducing Kernel Hilbert Spaces4.9 Poisson-Type Summation Formula over the Euclidean Space; 4.10 Functional Values-Based Shannon-Type Sampling (Euclidean Space); 4.11 Fourier Transformed Values-Based Shannon-Type Sampling (Euclidean Space); Part III: Preparatory Material for Multivariate Lattice Point Summation and Shannon-Type Sampling; 5. Preparatory Tools of Vector Analysis; 5.1 Cartesian Notation and Settings; 5.2 Spherical Notation and Settings; 5.3 Regular Regions and Integral Theorems; 6. Preparatory Tools of the Theory of Special Functions 6.1 Homogeneous Harmonic Polynomials6.2 Bessel Functions; 6.3 Asymptotic Expansions; 7. Preparatory Tools of Lattice Point Theory; 7.1 Lattices in Euclidean Spaces; 7.2 Figure Lattices in Euclidean Spaces; 7.3 Basic Results of the Geometry of Numbers; 7.4 Lattice Points Inside Spheres; 8. Preparatory Tools of Fourier Analysis; 8.1 Stationary Point Asymptotics; 8.2 Periodic Polynomials and Fourier Expansions; 8.3 Fourier Transform over Euclidean Spaces; 8.4 Periodization and Classical Poisson Summation Formula; 8.5 Gauss-Weierstrass Transform over Euclidean Spaces 8.6 Hankel Transform and Discontinuous IntegralsPart IV: Multivariate Euler-Type Summation Formulas over Regular Regions; 9. Euler-Green Function and Euler-Type Summation Formula; 9.1 Euler-Green Function; 9.2 Euler-Type Summation Formulas over Regular Regions Based on Euler-Green Functions; 9.3 Iterated Euler-Green Function; 9.4 Euler-Type Summation Formulas over Regular Regions Based on Iterated Euler-Green Functions; Part V: Bivariate Lattice Point/Ball Summation and Shannon-Type Sampling; 10. Hardy-Landau-Type Lattice Point Identities (Constant Weight)
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2020
• Extent: 1 online resource
• Subjects: 519.5/2; Sampling (Statistics); Lattice theory; Échantillonnage (Statistique); Théorie des treillis; Lattice theory; Sampling (Statistics); Electronic books; Electronic books
• Languages: English
• ISBNs: 1000756521; 9780429355103; 0429355106; 9781000757743; 1000757749; 9781000757132; 1000757137; 9781000756524
• Related ISBNs: 036737563X; 9780367375638
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from digital title page (viewed on March 20, 2020).
• 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.