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Convolution Operators and Factorization of Almost Periodic Matrix Functions

  • Book
  • © 2002

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Authors:
  1. Albrecht Böttcher

    1. Faculty of Mathematics, Technical University Chemnitz, Chemnitz, Germany

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  2. Yuri I. Karlovich

    1. Department of Mathematics, CINVESTAV of the I.P.N., Mexico D.F., Mexico

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    You can also search for this author in PubMed   Google Scholar

  3. Ilya M. Spitkovsky

    1. Department of Mathematics, College of William and Mary, Williamsburg, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Operator Theory: Advances and Applications (OT, volume 131)

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Convolution Operators and Their Symbols

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 1-25

  3. Introduction to Scalar Wiener-Hopf Operators

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 27-49

  4. Scalar Wiener-Hopf Operators with SAP Symbols

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 51-68

  5. Some Phenomena Caused by SAP Symbols

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 69-92

  6. Introduction to Matrix Wiener-Hopf Operators

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 93-106

  7. Factorizations of Matrix Functions

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 107-119

  8. Bohr Compactification

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 121-130

  9. Existence and Uniqueness of AP Factorization

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 131-154

  10. Matrix Wiener-Hopf Operators with APW Symbols

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 155-179

  11. Matrix Wiener-Hopf Operators with SAPW Symbols

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 181-206

  12. Left Versus Right Wiener-Hopf Factorization

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 207-225

  13. Corona Theorems

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 227-241

  14. The Portuguese Transformation

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 243-258

  15. Some Concrete Factorizations

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 259-279

  16. Scalar Trinomials

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 281-299

  17. Toeplitz Operators

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 301-321

  18. Zero-Order Pseudodifferential Operators

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 323-336

  19. Toeplitz Operators with SAP Symbols on Hardy Spaces

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 337-369

  20. Wiener-Hopf Operators with SAP Symbols on Lebesgue Spaces

    • Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky
    Pages 371-386
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Keywords

About this book

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

Authors and Affiliations

  • Faculty of Mathematics, Technical University Chemnitz, Chemnitz, Germany

    Albrecht Böttcher

  • Department of Mathematics, CINVESTAV of the I.P.N., Mexico D.F., Mexico

    Yuri I. Karlovich

  • Department of Mathematics, College of William and Mary, Williamsburg, USA

    Ilya M. Spitkovsky

Bibliographic Information

  • Book Title: Convolution Operators and Factorization of Almost Periodic Matrix Functions

  • Authors: Albrecht Böttcher, Yuri I. Karlovich, Ilya M. Spitkovsky

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8152-4

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 2002

  • Hardcover ISBN: 978-3-7643-6672-8Published: 01 February 2002

  • Softcover ISBN: 978-3-0348-9457-9Published: 23 October 2012

  • eBook ISBN: 978-3-0348-8152-4Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XI, 462

  • Topics: Operator Theory

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