Leiba Rodman 
Abstract Band Method via Factorization, Positive and Band Extensions of Multivariable Almost Periodic Matrix Functions, and Spectral Estimation [PDF ebook] 

Ủng hộ

New versions are developed of an abstract scheme, which are designed to provide a framework for solving a variety of extension problems. The abstract scheme is commonly known as the band method. The main feature of the new versions is that they express directly the conditions for existence of positive band extensions in terms of abstract factorizations (with certain additional properties). The results allow us to prove, among other things, that the band extension is continuous in an appropriate sense. Using the new versions of the abstract band method, we solve the positive extension problem for almost periodic matrix functions of several real variables with Fourier coefficients indexed in a given additive subgroup of the space of variables. This generality allows us to treat simultaneously many particular cases, for example the case of functions periodic in some variables and almost periodic in others. Necessary and sufficient conditions are given for the existence of positive extensions in terms of Toeplitz operators on Besikovitch spaces. Furthermore, when a solution exists a special extension (the band extension) is constructed which enjoys a maximum entropy property. A linear fractional parameterization of the set of all extensions is also provided. We interpret the obtained results (in the periodic case) in terms of existence of a multivariate autoregressive moving averages (ARMA) process with given autocorrelation coefficients, and identify its maximal prediction error. Another application concerns the solution of the positive extension problem in the context of Wiener algebra of infinite operator matrices. It includes the identification of the maximum entropy extension and a description of all positive extensions via a linear fractional formula. In the periodic case it solves a linear estimation problem for cyclostationary stochastic processes.

€86.11
phương thức thanh toán
Mua cuốn sách điện tử này và nhận thêm 1 cuốn MIỄN PHÍ!
định dạng PDF ● Trang 71 ● ISBN 9781470403607 ● Nhà xuất bản American Mathematical Society ● Có thể tải xuống 3 lần ● Tiền tệ EUR ● TÔI 6612958 ● Sao chép bảo vệ Adobe DRM
Yêu cầu trình đọc ebook có khả năng DRM

Thêm sách điện tử từ cùng một tác giả / Biên tập viên

50.053 Ebooks trong thể loại này