Convolution Operators and Factorization of Almost Periodic Matrix Functions 

Author:
 Karlovich, Yuri I. Rodman, Leiba Böttcher, Albrecht Spitkovsky, Ilya M. 
Series title:  Operator Theory: Advances and Applications Ser. 
ISBN:  9783034894579 
Publication Date:  Oct 2012 
Publisher:  Birkhäuser Boston

Book Format:  Paperback 
List Price:  USD $89.99 
Book Description:

Many problems of the engineering sciences, physics, and mathematics lead to con volution equations and their various modifications. Convolution equations on a halfline can be studied by having recourse to the methods and results of the theory of Toeplitz and WienerHopf operators. Convolutions by integrable kernels have continuous symbols and the Cauchy singular integral operator is the most prominent example of a convolution operator with a piecewise continuous symbol. The Fredholm...
More DescriptionMany problems of the engineering sciences, physics, and mathematics lead to con volution equations and their various modifications. Convolution equations on a halfline can be studied by having recourse to the methods and results of the theory of Toeplitz and WienerHopf operators. Convolutions by integrable kernels have continuous symbols and the Cauchy singular integral operator is the most prominent example of a convolution operator with a piecewise continuous symbol. The Fredholm theory of Toeplitz and WienerHopf operators with continuous and piecewise continuous (matrix) symbols is well presented in a series of classical and recent monographs. Symbols beyond piecewise continuous symbols have discontinuities of oscillating type. Such symbols emerge very naturally. For example, difference operators are nothing but convolution operators with almost periodic symbols: the operator defined by (A