Deguang Han's Books

Operator-Valued Measures, Dilations, and the Theory of Frames

By: Deguang Han, David R. Larson,Bei Liu,Rui Liu

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Operator-Valued Measures, Dilations, and the Theory of Frames

By: Deguang Han, David R. Larson,Bei Liu,Rui Liu

The authors develop elements of a general dilation theory for operator-valued measures. Hilbert space operator-valued measures are closely related to bounded linear maps on abelian von Neumann algebras, and some of their results include new dilation results for bounded linear maps that are not necessarily completely bounded, and from domain algebras that are not necessarily abelian. In the non-cb case the dilation space often needs to be a Banach space. They give applications to both the discrete and the continuous frame theory. There are natural associations between the theory of frames (including continuous frames and framings), the theory of operator-valued measures on sigma-algebras of sets, and the theory of continuous linear maps between -algebras. In this connection frame theory itself is identified with the special case in which the domain algebra for the maps is an abelian von Neumann algebra and the map is normal (i.e. ultraweakly, or weakly, or w*) continuous.

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American Mathematical Soc.

Published Date

ISBN 10

0821891723

ISBN 13

9780821891728

Frames, Bases and Group Representations

By: Deguang Han,David R. Larson

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Frames, Bases and Group Representations

By: Deguang Han,David R. Larson

This work develops an operator-theoretic approach to discrete frame theory on a separable Hilbert space. It is then applied to an investigation of the structural properties of systems of unitary operators on Hilbert space which are related to orthonormal wavelet theory. Also obtained are applications of frame theory to group representations, and of the theory of abstract unitary systems to frames generated by Gabor type systems.

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Page Count

111

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821820672

ISBN 13

9780821820674

Frames for Undergraduates

By: Deguang Han

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Frames for Undergraduates

By: Deguang Han

The early chapters contain the topics from linear algebra that students need to know in order to read the rest of the book. The later chapters are devoted to advanced topics, which allow students with more experience to study more intricate types of frames. Toward that end, a Student Presentation section gives detailed proofs of fairly technical results with the intention that a student could work out these proofs independently and prepare a presentation to a class or research group. The authors have also presented some stories in the Anecdotes section about how this material has motivated and influenced their students."--BOOK JACKET.

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314

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821842129

ISBN 13

9780821842126

Operator Theory, Operator Algebras, and Applications

The 25th Great Plains Operator Theory Symposium, June 7-12, 2005, University of Central Florida, Florida

By: Deguang Han,Palle E. T. Jørgensen,David R. Larson

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Operator Theory, Operator Algebras, and Applications

The 25th Great Plains Operator Theory Symposium, June 7-12, 2005, University of Central Florida, Florida

By: Deguang Han,Palle E. T. Jørgensen,David R. Larson

This book offers a presentation of some new trends in operator theory and operator algebras, with a view to their applications. It consists of separate papers written by some of the leading practitioners in the field. The content is put together by the three editors in a way that should help students and working mathematicians in other parts of the mathematical sciences gain insight into an important part of modern mathematics and its applications. While different specialist authors are outlining new results in this book, the presentations have been made user friendly with the aid of tutorial material. In fact, each paper contains three things: a friendly introduction with motivation, tutorial material, and new research. The authors have strived to make their results relevant to the rest of mathematics. A list of topics discussed in the book includes wavelets, frames and their applications, quantum dynamics, multivariable operator theory, $C*$-algebras, and von Neumann algebras. Some longer papers present recent advances on particular, long-standing problems such as extensions and dilations, the Kadison-Singer conjecture, and diagonals of self-adjoint operators.

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Page Count

440

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821839233

ISBN 13

9780821839232

Frames for Undergraduates

By: Deguang Han

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Frames for Undergraduates

By: Deguang Han

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Page Count

314

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821842129

ISBN 13

9780821842126

Frames, Bases and Group Representations

By: Deguang Han,David R. Larson

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Frames, Bases and Group Representations

By: Deguang Han,David R. Larson

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Page Count

111

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821820672

ISBN 13

9780821820674

Book's by Deguang Han

Operator-Valued Measures, Dilations, and the Theory of Frames

Operator-Valued Measures, Dilations, and the Theory of Frames

Frames, Bases and Group Representations

Frames, Bases and Group Representations

Frames for Undergraduates

Frames for Undergraduates

Operator Theory, Operator Algebras, and Applications

Operator Theory, Operator Algebras, and Applications

Frames for Undergraduates

Frames for Undergraduates

Frames, Bases and Group Representations

Frames, Bases and Group Representations

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