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25990 results in Abstract analysis

Page 1 of 1300

Nearly Invariant Subspaces and their Applications
  • Jonathan R. Partington
  • Coming soon
  • Expected online publication date:
    December 2026
    Print publication:
    31 December 2026
  • This book offers a comprehensive introduction to nearly invariant subspaces, a subject of active contemporary research within functional analysis. Written for graduate students in mathematical analysis and suitable as a reference for experienced researchers, the book surveys the historical development of nearly invariant subspaces from their origins in the study of kernels of Toeplitz operators and invariant subspaces of shift operators. It presents recent advances, including applications to the invariant subspace problem, to truncated Toeplitz operators, and to strongly continuous semigroups of operators. Although mostly concerned with operators on Hardy spaces, the book includes a discussion of the subject in the context of Bergman and Dirichlet spaces too. The book begins with a chapter recalling basic results in analysis and function theory, and each chapter contains a selection of accessible exercises to supplement the text.

Introduction to Radon Transforms
  • With Elements of Fractional Calculus and Harmonic Analysis
  • 2nd edition
  • Boris Rubin
  • Coming soon
  • Expected online publication date:
    November 2026
    Print publication:
    30 November 2026
  • This comprehensive introduction contains a thorough exploration of Radon transforms and related operators when the basic manifolds are the real Euclidean space, the unit sphere, and the real hyperbolic space. Radon-like transforms are discussed not only on smooth functions but also in the general context of Lebesgue spaces. Applications, open problems, and recent results are also included. The book will be useful for researchers in integral geometry, harmonic analysis, and related branches of mathematics. Fields of application include modern analysis, integral and convex geometry, and medical imaging. The text contains many examples and detailed proofs, making it accessible to graduate students and advanced undergraduates. The new edition includes four new chapters covering topics including integral geometry on lower-dimensional surfaces, tangency problems in integral geometry, and applications to convex geometry.

Periodic Elliptic Partial Differential Operators
  • The Main Structures
  • Volume 1
  • Peter Kuchment
  • Coming soon
  • Expected online publication date:
    September 2026
    Print publication:
    30 September 2026
  • The study of periodic partial differential equations has experienced significant growth in recent decades, driven by emerging applications in fields such as photonic crystals, metamaterials, fluid dynamics, carbon nanostructures, and topological insulators. This book provides a uniquely comprehensive overview for mathematicians, physicists, and material scientists engaged in the analysis and construction of periodic media. It describes all the mathematical objects, tools, problems, and techniques involved. Topics covered are central for areas such as spectral theory of PDEs, homogenization, condensed matter physics and optics. Although it is not a textbook, some basic proofs, background material, and references to an extensive bibliography providing pointers to the wider literature are included to allow graduate students to access the content.

Dilation and Model Theory for Pairs of Commuting Contraction Operators
  • Joseph A. Ball, Haripada Sau
  • Coming soon
  • Expected online publication date:
    July 2026
    Print publication:
    31 July 2026
  • Exactly a decade after the publication of the Sz.-Nagy dilation theorem, Tsuyoshi Ando proved that, just like for a single contractive operator, every commuting pair of Hilbert-space contractions can be lifted to a commuting isometric pair. Although the inspiration for Ando's proof comes from the elegant construction of Schäffer for the single-variable case, his proof did not shed much light on the explicit nature of the dilation operators and the dilation space as did the original Schäffer and Douglas constructions for a single contraction. Consequently, there has been little follow-up in the direction of a more systematic extension of the Sz.-Nagy–Foias dilation and model theory to the bivariate setting. Sixty years since the appearance of Ando's first step comes this thorough systematic treatment of a dilation and model theory for pairs of commuting contractions.

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