Publication list for Ross, William

Publication list for Ross, William

  • The Cauchy Transform
    Base Product Code Keyword List: surv; SURV; surv/125; SURV/125; surv-125; SURV-125
    Online Product Code: SURV/125.E
    Title (HTML): The Cauchy Transform
    Author(s) (Product display): Joseph A. Cima; Alec L. Matheson; William T. Ross
    Affiliation(s) (HTML):
    Abstract:

    The Cauchy transform of a measure on the circle is a subject of both classical and current interest with a sizable literature. This book is a thorough, well-documented, and readable survey of this literature and includes full proofs of the main results of the subject. This book also covers more recent perturbation theory as covered by Clark, Poltoratski, and Aleksandrov and contains an in-depth treatment of Clark measures.

    Book Series Name: Mathematical Surveys and Monographs
    Volume: 125
    Publication Month and Year: 2006-03-28
    Copyright Year: 2006
    Page Count: 272
    Online ISBN 13: 978-1-4704-1352-1
    Online ISSN: 0076-5376
    Primary MSC: 30; 32; 47; 46
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    SXG Subject: AN
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/surv-125
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    Reviews:

    Proofs are presented very carefully, so that the whole material becomes accessible to any graduate student interested in analysis. Experienced researchers will also be thankful to the authors for having presented them this material for the first time. We recommend this survey to any person interested in function theory and operator theory on the disk.

    -- Zentralblatt MATH

    The book is user-friendly it is clearly written, at an agreeable pace. Many of the deepest results of the theory are afforded complete treatments. Scattered throughout are mentions of related results, with references to the literature. The authors are thorough and meticulous in their citation of references.

    -- Mathematical Reviews

    ...contains a wealth of interesting results, presented in an attractive and readable style...

    -- Bulletin of the LMS

    Combining both classical and recent result, the book presents a great interest for students, teachers and researchers interested mainly in functional analysis methods in complex analysis. The topics are presented in an elegant manner, with many comments, detours and historical references. The result is a fine book that deserves to be on the bookshelf of each analyst.

    -- Studia Universitatis Babes-Bolyai, Mathematica

  • The Backward Shift on the Hardy Space
    Base Product Code Keyword List: surv; SURV; surv/79; SURV/79; surv-79; SURV-79
    Print Product Code: SURV/79
    Online Product Code: SURV/79.E
    Title (HTML): The Backward Shift on the Hardy Space
    Author(s) (Product display): Joseph A. Cima; William T. Ross
    Affiliation(s) (HTML): University of North Carolina, Chapel Hill, Chapel Hill, NC; University of Richmond, Richmond, VA
    Abstract:

    Shift operators on Hilbert spaces of analytic functions play an important role in the study of bounded linear operators on Hilbert spaces since they often serve as models for various classes of linear operators. For example, “parts” of direct sums of the backward shift operator on the classical Hardy space \(H^2\) model certain types of contraction operators and potentially have connections to understanding the invariant subspaces of a general linear operator.

    This book is a thorough treatment of the characterization of the backward shift invariant subspaces of the well-known Hardy spaces \(H^{p}\). The characterization of the backward shift invariant subspaces of \(H^{p}\) for \(1 < p < \infty\) was done in a 1970 paper of R. Douglas, H. S. Shapiro, and A. Shields, and the case \(0 < p \le 1\) was done in a 1979 paper of A. B. Aleksandrov which is not well known in the West. This material is pulled together in this single volume and includes all the necessary background material needed to understand (especially for the \(0 < p < 1\) case) the proofs of these results.

    Several proofs of the Douglas-Shapiro-Shields result are provided so readers can get acquainted with different operator theory and theory techniques: applications of these proofs are also provided for understanding the backward shift operator on various other spaces of analytic functions. The results are thoroughly examined. Other features of the volume include a description of applications to the spectral properties of the backward shift operator and a treatment of some general real-variable techniques that are not taught in standard graduate seminars. The book includes references to works by Duren, Garnett, and Stein for proofs and a bibliography for further exploration in the areas of operator theory and functional analysis.

    Book Series Name: Mathematical Surveys and Monographs
    Volume: 79
    Publication Month and Year: 2000-06-13
    Copyright Year: 2000
    Page Count: 199
    Cover Type: Hardcover
    Print ISBN-13: 978-0-8218-2083-4
    Online ISBN 13: 978-1-4704-1306-4
    Print ISSN: 0076-5376
    Online ISSN: 0076-5376
    Primary MSC: 47
    Secondary MSC: 46
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    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/surv-79
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    Readership:

    Advanced graduate students with a background in basic functional analysis, complex analysis and the basics of the theory of Hardy spaces; professional mathematicians interested in operator theory and functional analysis.

    Reviews:

    The book has been carefully written and contains a wealth of information … It will probably appeal most to those with an interest in the interplay between operator theory and modern function theory.

    -- Bulletin of the LMS

  • Recent Progress on Operator Theory and Approximation in Spaces of Analytic Functions
    Base Product Code Keyword List: conm; CONM; conm/679; CONM/679; conm-679; CONM-679
    Print Product Code: CONM/679
    Online Product Code: CONM/679.E
    Title (HTML): Recent Progress on Operator Theory and Approximation in Spaces of Analytic Functions
    Author/Editor Label (optional): Edited by
    Author(s) (Product display): Catherine Bénéteau; Alberto A. Condori; Constanze Liaw; William T. Ross; Alan A. Sola
    Affiliation(s) (HTML): University of South Florida, Tampa, FL; Florida Gulf Coast University, Fort Myers, FL; Baylor University, Waco, TX; University of Richmond, Richmond, VA; University of South Florida, Tampa, FL
    Abstract:

    This volume contains the Proceedings of the Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, held from June 29–July 3, 2015, at the Institut Mittag-Leffler, Djursholm, Sweden.

    The conference brought together experienced researchers and promising young mathematicians from many countries to discuss recent progress made in function theory, model spaces, completeness problems, and Carleson measures.

    This volume contains articles covering cutting-edge research questions, as well as longer survey papers and a report on the problem session that contains a collection of attractive open problems in complex and harmonic analysis.

    Book Series Name: Contemporary Mathematics
    Volume: 679
    Publication Month and Year: 2016-12-21
    Copyright Year: 2016
    Page Count: 217
    Cover Type: Softcover
    Print ISBN-13: 978-1-4704-2305-6
    Online ISBN 13: 978-1-4704-3627-8
    Print ISSN: 0271-4132
    Online ISSN: 0271-4132
    Primary MSC: 11; 30; 35; 47
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    Readership:

    Graduate students and research mathematicians interested in operator theory and complex analysis.

    Cover Image URL: ~~FreeAttachments/conm-679-cov.jpg
  • Invariant Subspaces of the Shift Operator
    Base Product Code Keyword List: conm; CONM; conm/638; CONM/638; conm-638; CONM-638
    Print Product Code: CONM/638
    Online Product Code: CONM/638.E
    Title (HTML): Invariant Subspaces of the Shift Operator
    Author/Editor Label (optional): Edited by
    Author(s) (Product display): Javad Mashreghi; Emmanuel Fricain; William Ross
    Affiliation(s) (HTML): Laval University, Quebec, Canada; Université Lille 1, Villeneuve d’Ascq, France; University of Richmond, Richmond, VA
    Publisher Blurb: A co-publication of the AMS and Centre de Recherches Mathématiques
    Abstract:

    This volume contains the proceedings of the CRM Workshop on Invariant Subspaces of the Shift Operator, held August 26–30, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada.

    The main theme of this volume is the invariant subspaces of the shift operator (or its adjoint) on certain function spaces, in particular, the Hardy space, Dirichlet space, and de Branges–Rovnyak spaces.

    These spaces, and the action of the shift operator on them, have turned out to be a precious tool in various questions in analysis such as function theory (Bieberbach conjecture, rigid functions, Schwarz–Pick inequalities), operator theory (invariant subspace problem, composition operator), and systems and control theory.

    Of particular interest is the Dirichlet space, which is one of the classical Hilbert spaces of holomorphic functions on the unit disk. From many points of view, the Dirichlet space is an interesting and challenging example of a function space. Though much is known about it, several important open problems remain, most notably the characterization of its zero sets and of its shift-invariant subspaces.

    Book Series Name: Contemporary Mathematics
    Volume: 638
    Publication Month and Year: 2015-04-20
    Copyright Year: 2015
    Page Count: 317
    Cover Type: Softcover
    Print ISBN-13: 978-1-4704-1045-2
    Online ISBN 13: 978-1-4704-2341-4
    Print ISSN: 0271-4132
    Online ISSN: 0271-4132
    Primary MSC: 47; 30; 31; 32
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    Publisher (non-AMS): A co-publication of the AMS and Centre de Recherches Mathématiques
    SXG Subject: AN
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    Print Add to Cart URL: /some/url/at/AMS/CONM-638
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    Readership:

    Graduate students and research mathematicians interested in operator theory and function spaces.

  • Generalized Analytic Continuation
    Base Product Code Keyword List: ulect; ULECT; ulect/25; ULECT/25; ulect-25; ULECT-25
    Print Product Code: ULECT/25
    Online Product Code: ULECT/25.E
    Title (HTML): Generalized Analytic Continuation
    Author(s) (Product display): William T. Ross; Harold S. Shapiro
    Affiliation(s) (HTML): University of Richmond, Richmond, VA; Royal Institute of Technology, Stockholm, Sweden
    Abstract:

    The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. This book addresses the following questions: (1) When can we say, in some reasonable way, that component functions of a meromorphic function on a disconnected domain, are “continuations” of each other? (2) What role do such “continuations” play in certain aspects of approximation theory and operator theory? The authors use the strong analogy with the summability of divergent series to motivate the subject. In this vein, for instance, theorems can be described as being “Abelian” or “Tauberian”. The introductory overview carefully explains the history and context of the theory.

    The authors begin with a review of the works of Poincaré, Borel, Wolff, Walsh, and Gončar, on continuation properties of “Borel series” and other meromorphic functions that are limits of rapidly convergent sequences of rational functions. They then move on to the work of Tumarkin, who looked at the continuation properties of functions in the classical Hardy space of the disk in terms of the concept of “pseudocontinuation”. Tumarkin's work was seen in a different light by Douglas, Shapiro, and Shields in their discovery of a characterization of the cyclic vectors for the backward shift operator on the Hardy space. The authors cover this important concept of “pseudocontinuation” quite thoroughly since it appears in many areas of analysis. They also add a new and previously unpublished method of “continuation” to the list, based on formal multiplication of trigonometric series, which can be used to examine the backward shift operator on many spaces of analytic functions. The book attempts to unify the various types of “continuations” and suggests some interesting open questions.

    Book Series Name: University Lecture Series
    Volume: 25
    Publication Month and Year: 2002-04-17
    Copyright Year: 2002
    Page Count: 149
    Cover Type: Softcover
    Print ISBN-13: 978-0-8218-3175-5
    Online ISBN 13: 978-1-4704-2172-4
    Print ISSN: 1047-3998
    Online ISSN: 1047-3998
    Primary MSC: 30; 47
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    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/ulect-25
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    Readership:

    Graduate students and research mathematicians interested in functions of a complex variable, approximation theory, and operator theory.

    Reviews:

    Interesting and well written book … an extensive and useful bibliography …

    -- Zentralblatt MATH

    Interesting and inspiring small book … can be recommended as a source of many interesting and well-motivated open problems.

    -- Mathematical Reviews