Ebook: Convolution Operators and Factorization of Almost Periodic Matrix Functions
- Tags: Operator Theory
- Series: Operator Theory: Advances and Applications 131
- Year: 2002
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
Many problems of the engineering sciences, physics, and mathematics lead to con volution equations and their various modifications. Convolution equations on a half-line can be studied by having recourse to the methods and results of the theory of Toeplitz and Wiener-Hopf 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 Wiener-Hopf 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
Content:
Front Matter....Pages i-xi
Convolution Operators and Their Symbols....Pages 1-25
Introduction to Scalar Wiener-Hopf Operators....Pages 27-49
Scalar Wiener-Hopf Operators with SAP Symbols....Pages 51-68
Some Phenomena Caused by SAP Symbols....Pages 69-92
Introduction to Matrix Wiener-Hopf Operators....Pages 93-106
Factorizations of Matrix Functions....Pages 107-119
Bohr Compactification....Pages 121-130
Existence and Uniqueness of AP Factorization....Pages 131-154
Matrix Wiener-Hopf Operators with APW Symbols....Pages 155-179
Matrix Wiener-Hopf Operators with SAPW Symbols....Pages 181-206
Left Versus Right Wiener-Hopf Factorization....Pages 207-225
Corona Theorems....Pages 227-241
The Portuguese Transformation....Pages 243-258
Some Concrete Factorizations....Pages 259-279
Scalar Trinomials....Pages 281-299
Toeplitz Operators....Pages 301-321
Zero-Order Pseudodifferential Operators....Pages 323-336
Toeplitz Operators with SAP Symbols on Hardy Spaces....Pages 337-369
Wiener-Hopf Operators with SAP Symbols on Lebesgue Spaces....Pages 371-386
Hankel Operators on Besicovitch Spaces....Pages 387-394
Generalized AP Factorization....Pages 395-405
Canonical Wiener-Hopf Factorization via Corona Problems....Pages 407-426
Canonical APW Factorization via Corona Problems....Pages 427-440
Back Matter....Pages 441-464
Content:
Front Matter....Pages i-xi
Convolution Operators and Their Symbols....Pages 1-25
Introduction to Scalar Wiener-Hopf Operators....Pages 27-49
Scalar Wiener-Hopf Operators with SAP Symbols....Pages 51-68
Some Phenomena Caused by SAP Symbols....Pages 69-92
Introduction to Matrix Wiener-Hopf Operators....Pages 93-106
Factorizations of Matrix Functions....Pages 107-119
Bohr Compactification....Pages 121-130
Existence and Uniqueness of AP Factorization....Pages 131-154
Matrix Wiener-Hopf Operators with APW Symbols....Pages 155-179
Matrix Wiener-Hopf Operators with SAPW Symbols....Pages 181-206
Left Versus Right Wiener-Hopf Factorization....Pages 207-225
Corona Theorems....Pages 227-241
The Portuguese Transformation....Pages 243-258
Some Concrete Factorizations....Pages 259-279
Scalar Trinomials....Pages 281-299
Toeplitz Operators....Pages 301-321
Zero-Order Pseudodifferential Operators....Pages 323-336
Toeplitz Operators with SAP Symbols on Hardy Spaces....Pages 337-369
Wiener-Hopf Operators with SAP Symbols on Lebesgue Spaces....Pages 371-386
Hankel Operators on Besicovitch Spaces....Pages 387-394
Generalized AP Factorization....Pages 395-405
Canonical Wiener-Hopf Factorization via Corona Problems....Pages 407-426
Canonical APW Factorization via Corona Problems....Pages 427-440
Back Matter....Pages 441-464
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