The Classical Moment Problem And Some Related Questions In Analysis
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| Author | : N.I. Akhiezer |
| Publisher | : SIAM |
| Total Pages | : 267 |
| Release | : 2020-12-01 |
| Genre | : Mathematics |
| ISBN | : 1611976391 |
The mathematical theory for many application areas depends on a deep understanding of the theory of moments. These areas include medical imaging, signal processing, computer visualization, and data science. The problem of moments has also found novel applications to areas such as control theory, image analysis, signal processing, polynomial optimization, and statistical big data. The Classical Moment Problem and Some Related Questions in Analysis presents a unified treatment of the development of the classical moment problem from the late 19th century to the middle of the 20th century. Important connections between the moment problem and many branches of analysis are presented. In this self-contained text, readers will find a unified exposition of important classical results, which are difficult to read in the original journals, as well as a strong foundation for many areas in modern applied mathematics. Researchers in areas that use techniques developed for the classical moment problem will find the book of interest.
| Author | : N. I. Akhiezer |
| Publisher | : Courier Dover Publications |
| Total Pages | : 273 |
| Release | : 2020-12-16 |
| Genre | : Mathematics |
| ISBN | : 0486845559 |
This text provides a classic treatment of issues associated with the moment problem that also involve linear algebra, probability theory, stochastic processes, quantum fields, signal processing, and more. 1965 edition.
| Author | : Naum Ilʹich Akhiezer |
| Publisher | : |
| Total Pages | : 253 |
| Release | : 1977 |
| Genre | : |
| ISBN | : |
| Author | : Naum Ilʹich Akhiezer |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1965 |
| Genre | : Functional analysis |
| ISBN | : 9780028402307 |
| Author | : Naum Ilʹich Akhiezer |
| Publisher | : |
| Total Pages | : |
| Release | : |
| Genre | : Moment spaces |
| ISBN | : |
| Author | : Naum Ilʹich Akhiezer |
| Publisher | : |
| Total Pages | : 253 |
| Release | : 1965 |
| Genre | : Functional analysis |
| ISBN | : |
| Author | : Naum Ilʹich Akhiezer |
| Publisher | : |
| Total Pages | : 253 |
| Release | : 1965 |
| Genre | : Spectral theory (Mathematics) |
| ISBN | : |
| Author | : Naum Ilʹich Akhiezer |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1965 |
| Genre | : Theory of distributions (Functional analysis) |
| ISBN | : |
| Author | : Naum Il'ich AKHIEZER |
| Publisher | : |
| Total Pages | : 253 |
| Release | : 1965 |
| Genre | : |
| ISBN | : |
| Author | : Daniel Alpay |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 306 |
| Release | : 2012-07-25 |
| Genre | : Mathematics |
| ISBN | : 3034804288 |
The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.
