Constructive Methods of Wiener-Hopf Factorization
Home > Mathematics and Science Textbooks > Mathematics > Algebra > Constructive Methods of Wiener-Hopf Factorization
Constructive Methods of Wiener-Hopf Factorization

Constructive Methods of Wiener-Hopf Factorization

|
     0     
5
4
3
2
1




Out of Stock


Notify me when this book is in stock
About the Book

The main part of this paper concerns Toeplitz operators of which the symbol W is an m x m matrix function defined on a disconnected curve r. The curve r is assumed to be the union of s + 1 nonintersecting simple smooth closed contours rOo r *...* rs which form the positively l oriented boundary of a finitely connected bounded domain in t. Our main requirement on the symbol W is that on each contour rj the function W is the restriction of a rational matrix function Wj which does not have poles and zeros on rj and at infinity. Using the realization theorem from system theory (see. e. g . * [1]. Chapter 2) the rational matrix function Wj (which differs from contour to contour) may be written in the form 1 (0. 1) W . (A) = I + C. (A - A. f B. A E r* J J J J J where Aj is a square matrix of size nj x n* say. B and C are j j j matrices of sizes n. x m and m x n . * respectively. and the matrices A. J x J J and Aj = Aj - BjC have no eigenvalues on r . (In (0. 1) the functions j j Wj are normalized to I at infinity.

Table of Contents:
I: Canonical and Minimal Factorization.- Editorial introduction.- Left Versus Right Canonical Factorization.- 1. Introduction.- 2. Left and right canonical Wiener-Hopf factorization.- 3. Application to singular integral operators.- 4. Spectral and antispectral factorization on the unit circle.- 5. Symmetrized left and right canonical spectral factorization on the imaginary axis.- References.- Wiener-Hopf Equations With Symbols Analytic In A Strip.- 0. Introduction.- I. Realization.- 1. Preliminaries.- 2. Realization triples.- 3. The realization theorem.- 4. Construction of realization triples.- 5. Basic properties of realization triples.- II. Applications.- 1. Inverse Fourier transforms.- 2. Coupling.- 3. Inversion and Fredholm properties.- 4. Canonical Wiener-Hopf factorization.- 5. The Riemann-Hilbert boundary value problem.- References.- On Toeplitz and Wiener-Hopf Operators with Contour-Wise Rational Matrix and Operator Symbols.- 0. Introduction.- 1. Indicator.- 2. Toeplitz operators on compounded contours.- 3. Proof of the main theorems.- 4. The barrier problem.- 5. Canonical factorization.- 6. Unbounded domains.- 7. The pair equation.- 8. Wiener-Hopf equation with two kernels.- 9. The discrete case.- References.- Canonical Pseudo-Spectral Factorization and Wiener-Hopf Integral Equations.- 0. Introduction.- 1. Canonical pseudo-spectral factorizations.- 2. Pseudo-?-spectral subspaces.- 3. Description of all canonical pseudo-?-spectral factorizations.- 4. Non-negative rational matrix functions.- 5. Wiener-Hopf integral equations of non-normal type.- 6. Pairs of function spaces of unique solvability.- References.- Minimal Factorization of Integral operators and Cascade Decompositions of Systems.- 0. Introduction.- I. Main results.- 1. Minimal representation and degree.- 2. Minimal factorization (1).- 3. Minimal factorization of Volterra integral operators (1).- 4. Stationary causal operators and transfer functions.- 5. SB-minimal factorization (1).- 6. SB-minimal factorization in the class (USB)..- 7. Analytic semi-separable kernels.- 8. LU- and UL-factorizations (1).- II. Cascade decomposition of systems.- 1. Preliminaries about systems with boundary conditions.- 2. Cascade decompositions.- 3. Decomposing projections.- 4. Main decomposition theorems.- 5. Proof of Theorem II.4.1.- 6. Proof of Theorem II.4.2.- 7. Proof of Theorem II.4.3.- 8. Decomposing projections for inverse systems..- III. Proofs of the main theorems.- 1. A factorization lemma.- 2. Minimal factorization (2).- 3. SB-minimal factorization (2).- 4. Proof of Theorem I.6.1.- 5. Minimal factorization of Volterra integral operators (2).- 6. Proof of Theorem I.4.1.- 7. A remark about minimal factorization and inversion.- 8. LU- and UL-f actorizations (2).- 9. Causal/anticausal decompositions.- References.- II: Non-Canonical Wiener-Hopf Factorization.- Editorial introduction.- Explicit Wiener-Hopf Factorization and Realization.- 0. Introduction.- 1. Preliminaries.- 1. Peliminaries about transfer functions.- 2. Preliminaries about Wiener-Hopf factorization.- 3. Reduction of factorization to nodes with centralized singularities.- II. Incoming characteristics.- 1. Incoming bases.- 2. Feedback operators related to incoming bases.- 3. Factorization with non-negative indices.- III. Outgoing characteristics.- 1. Outgoing bases.- 2. Output injection operators related to outgoing bases.- 3. Factorization with non-positive indices.- IV. Main results.- 1. Intertwining relations for incoming and outgoing data.- 2. Dilation to a node with centralized singularities.- 3. Main theorem and corollaries.- References,.- Invariants for Wiener-Hopf Equivalence of Analytic Operator Functions.- 1. Introduction and main result.- 2. Simple nodes with centralized singularities.- 3. Multiplication by plus and minus terms.- 4. Dilation.- 5. Spectral characteristics of transfer functions: outgoing spaces.- 6. Spectral characteristics of transfer functions: incoming spaces.- 7. Spectral characteristics and Wiener-Hopf equivalence.- References.- Multiplication by Diagonals and Reduction to Canonical Factorization.- 1. Introduction.- 2. Spectral pairs associated with products of nodes.- 3. Multiplication by diagonals.- References.- Symmetric Wiener-Hopf Factorization of Self-Adjoint Rational Matrix Functions and Realization.- 0. Introduction and summary.- 1. Introduction.- 2. Summary.- I. Wiener-Hopf factorization.- 1. Realizations with centralized singularities..- 2. Incoming data and related feedback operators.- 3. Outgoing data and related output injection operators.- 4. Dilation to realizations with centralized singularities.- 5. The final formulas.- II. Symmetric Wiener-Hopf factorization.- 1. Duality between incoming and outgoing operators.- 2. The basis in (C and duality between the feedback operators and the output injection operators.- 3. Proof of the main theorems.- References.


Best Sellers


Product Details
  • ISBN-13: 9783764318260
  • Publisher: Birkhauser Verlag AG
  • Publisher Imprint: Birkhauser Verlag AG
  • Language: English
  • ISBN-10: 3764318260
  • Publisher Date: 01 Jan 1986
  • Binding: Hardback
  • Weight: 940 gr


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Constructive Methods of Wiener-Hopf Factorization
Birkhauser Verlag AG -
Constructive Methods of Wiener-Hopf Factorization
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Constructive Methods of Wiener-Hopf Factorization

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    New Arrivals

    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!