Functional Equations and Characterization Problems on Locally Compact Abelian Groups (Record no. 50386)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03391nam a22004095a 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783037195451 |
| 100 1# - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Feldman, Gennadiy, |
| 245 10 - TITLE STATEMENT | |
| Title | Functional Equations and Characterization Problems on Locally Compact Abelian Groups |
| Statement of responsibility, etc | Gennadiy Feldman |
| 260 3# - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Zuerich, Switzerland : |
| Name of publisher | European Mathematical Society Publishing House, |
| Year of publication | 2008 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 1 online resource (268 pages) |
| 490 0# - SERIES STATEMENT | |
| Series statement | EMS Tracts in Mathematics (ETM) |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This book deals with the characterization of probability distributions. It is well known that both the sum and the difference of two Gaussian independent random variables with equal variance are independent as well. The converse statement was proved independently by M. Kac and S. N. Bernstein. This result is a famous example of a characterization theorem. In general, characterization problems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions in these variables. In recent years, a great deal of attention has been focused upon generalizing the classical characterization theorems to random variables with values in various algebraic structures such as locally compact Abelian groups, Lie groups, quantum groups, or symmetric spaces. The present book is aimed at the generalization of some well-known characterization theorems to the case of independent random variables taking values in a locally compact Abelian group X. The main attention is paid to the characterization of the Gaussian and the idempotent distribution (group analogs of the Kac–Bernstein, Skitovich–Darmois, and Heyde theorems). The solution of the corresponding problems is reduced to the solution of some functional equations in the class of continuous positive definite functions defined on the character group of X. Group analogs of the Cramér and Marcinkiewicz theorems are also studied. The author is an expert in algebraic probability theory. His comprehensive and self-contained monograph is addressed to mathematicians working in probability theory on algebraic structures, abstract harmonic analysis, and functional equations. The book concludes with comments and unsolved problems that provide further stimulation for future research in the theory. |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Probability & statistics |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Probability theory and stochastic processes |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Abstract harmonic analysis |
| 650 07 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Statistics |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Feldman, Gennadiy, |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://doi.org/10.4171/045 |
| 856 42 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://www.ems-ph.org/img/books/feldman_mini.jpg |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | E-BOOKS |
| 264 #1 - | |
| -- | Zuerich, Switzerland : |
| -- | European Mathematical Society Publishing House, |
| -- | 2008 |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|
| IMSc Library | EBK13762 | https://doi.org/10.4171/045 | E-BOOKS |