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Kac-Bernstein and Skitovich-Darmois Theorem / Dieudonné Serganova.
Material type:
TextLanguage: English Publication details: India : Phoenix, 2023.Edition: 1st edDescription: xii, 245 p. : 24 cmISBN: - 9789392359392
- 512.743 SER
Contents:
Summary: This monograph presents the classical Kac–Bernstein and Skitovich–Darmois characterization theorems, which identify the Gaussian (normal) distribution through independence properties of random variables. It develops the mathematical foundations of these theorems, provides rigorous proofs, discusses extensions to locally compact Abelian groups, and examines related functional equations and applications in probability theory and harmonic analysis.
Preliminaries. Gaussian Distributions on locally compact Abelian groups. The Kac–Bernstein Theorem for locally compact Abelian groups. The Skitovich–Darmois Theorem for locally compact Abelian groups. The Skitovich–Darmois Theorem for locally compact Abelian groups. (the general case). The Heyde Theorem for locally compact Abelian groups.
| Item type | Current library | Collection | Shelving location | Call number | Status | Barcode | |
|---|---|---|---|---|---|---|---|
Reference
|
Kalaignar Centenary Library Madurai | ENGLISH-REFERENCE BOOKS | மூன்றாம் தளம் / Third floor | 512.743 SER (Browse shelf(Opens below)) | Not for loan | 315593 | |
| English Books | Kalaignar Centenary Library Madurai | ENGLISH - LENDING BOOKS | மூன்றாம் தளம் / Third floor | 512.743 SER (Browse shelf(Opens below)) | Available | 315594 | |
| English Books | Kalaignar Centenary Library Madurai | ENGLISH - LENDING BOOKS | மூன்றாம் தளம் / Third floor | 512.743 SER (Browse shelf(Opens below)) | Available | 315595 |
Includes index.
Preliminaries. Gaussian Distributions on locally compact Abelian groups. The Kac–Bernstein Theorem for locally compact Abelian groups. The Skitovich–Darmois Theorem for locally compact Abelian groups. The Skitovich–Darmois Theorem for locally compact Abelian groups. (the general case). The Heyde Theorem for locally compact Abelian groups.
This monograph presents the classical Kac–Bernstein and Skitovich–Darmois characterization theorems, which identify the Gaussian (normal) distribution through independence properties of random variables. It develops the mathematical foundations of these theorems, provides rigorous proofs, discusses extensions to locally compact Abelian groups, and examines related functional equations and applications in probability theory and harmonic analysis.