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Operator Theory

An Introduction to Quiver Representations

This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on Auslander-Reiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly w...

Random Operators: Disorder Effects on Quantum Spectra and Dynamics

This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization—presented here via the fractional moment method, up to recent results on resonant delocaliza...

Topics in Differential and Integral Equations and Operator Theory (Softcover reprint of the original 1st ed. 1983)

  • Krein |
  • 2013 |
  • djvu |
  • 2.93MB |
  • 310pages

In this volume three important papers of M.G. Krein appear for the first time in English translation. Each of them is a short self-contained monograph, each a masterpiece of exposition. Although two of them were written more than twenty years ago, the passage of time has not decreased their value. They are as fresh and vital as ...

Positive Linear Maps of Operator Algebras (2013th Edition)

This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous r...

Spectral Theory of Operators on Hilbert Spaces (1st Edition)

This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate...

PSEUDODIFFERENTIAL OPERATORS

This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. It presents the necessary material on Fourier transformation and distribution theory, the basic calculus of pseudodifferential operators on the n-dimen...

The Elements of Operator Theory (2nd Edition)

"The author endeavors to present the concepts and ideas as an alternative to the computational approach, trying to avoid long calculations by stressing the mathematical thoughts behind the statements. . . . many problems [are] stated throughout the book, very often accompanied by hints."—Mathematical Reviews (review of the first...

Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice (1st Edition)

This volume presents the state of the art of new developments, and some interesting and relevant applications of the OWA (ordered weighted averaging) operators. The OWA operators were introduced in the early 1980s by Ronald R. Yager as a conceptually and numerically simple, easily implementable, yet extremely powerful general ag...

Integral Equations with Difference Kernels on Finite Intervals: Second Edition, Revised and Extended (2nd revised and extended ed. 2015)

Provides a new and effective method for solving integral equations with difference kernelsUses the results obtained to investigate a number of theoretical and applied problemsPresents solutions to some well-known problems, in particular the M. Kac problems and a new form of the Levy-Ito equalityStudies a number of essential exam...

One-Dimensional Linear Singular Integral Equations: Volume II General Theory and Applications (Softcover reprint of the original 1st ed. 1992)

This monograph is the second volume of a graduate text book on the modern theory of linear one-dimensional singular integral equations. Both volumes may be regarded as unique graduate text books. Singular integral equations attract more and more attention since this class of equations appears in numerous applications, and also b...