Jingzhi Tie's Books

Laguerre Calculus and Its Applications on the Heisenberg Group

By: Carlos A. Berenstein,Der-chen E. Chang,Jingzhi Tie

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Laguerre Calculus and Its Applications on the Heisenberg Group

By: Carlos A. Berenstein,Der-chen E. Chang,Jingzhi Tie

For nearly two centuries, the relation between analytic functions of one complex variable, their boundary values, harmonic functions, and the theory of Fourier series has been one of the central topics of study in mathematics. The topic stands on its own, yet also provides very useful mathematical applications. This text provides a self-contained introduction to the corresponding questions in several complex variables: namely, analysis on the Heisenberg group and the study of the solutions of the boundary Cauchy-Riemann equations. In studying this material, readers are exposed to analysis in non-commutative compact and Lie groups, specifically the rotation group and the Heisenberg groups-both fundamental in the theory of group representations and physics. Introduced in a concrete setting are the main ideas of the Calderón-Zygmund-Stein school of harmonic analysis. Also considered in the book are some less conventional problems of harmonic and complex analysis, in particular, the Morera and Pompeiu problems for the Heisenberg group, which relates to questions in optics, tomography, and engineering. The book was borne of graduate courses and seminars held at the University of Maryland (College Park), the University of Toronto (ON), Georgetown University (Washington, DC), and the University of Georgia (Athens). Readers should have an advanced undergraduate understanding of Fourier analysis and complex analysis in one variable.

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Page Count

333

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821827618

ISBN 13

9780821827611

The Sub-Laplacian Operators of Some Model Domains

By: Der-Chen Chang,Jingzhi Tie

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The Sub-Laplacian Operators of Some Model Domains

By: Der-Chen Chang,Jingzhi Tie

The book studies sub-Laplacian operators on a family of model domains in C^{n+1}, which is a good point-wise model for a $CR$ manifold with non-degenerate Levi form. A considerable amount of study has been devoted to partial differential operators constructed from non-commuting vector fields, in which the non-commutativity plays an essential role in determining the regularity properties of the operators.

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Page Count

266

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110642999

ISBN 13

9783110642995

A Critical History of New Music in China

By: Jingzhi Liu

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A Critical History of New Music in China

By: Jingzhi Liu

By the end of the nineteenth century, Chinese culture had fallen into a stasis, and intellectuals began to go abroad for new ideas. What emerged was an exciting musical genre that C. C. Liu terms "new music." With no direct ties to traditional Chinese music, "new music" reflects the compositional techniques and musical idioms of eighteenth- and nineteenth-century European styles. Liu traces the genesis and development of "new music" throughout the twentieth century, deftly examining the social and political forces that shaped "new music" and its uses by political activists and the government.

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Page Count

962

Publisher

Chinese University Press

Published Date

ISBN 10

9629963604

ISBN 13

9789629963606

The Sub-Laplacian Operators of Some Model Domains

By: Der-Chen Chang,Jingzhi Tie

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The Sub-Laplacian Operators of Some Model Domains

By: Der-Chen Chang,Jingzhi Tie

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Solve jigsaw puzzle

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Page Count

266

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110642999

ISBN 13

9783110642995

Book's by Jingzhi Tie

Laguerre Calculus and Its Applications on the Heisenberg Group

Laguerre Calculus and Its Applications on the Heisenberg Group

The Sub-Laplacian Operators of Some Model Domains

The Sub-Laplacian Operators of Some Model Domains

A Critical History of New Music in China

A Critical History of New Music in China

The Sub-Laplacian Operators of Some Model Domains

The Sub-Laplacian Operators of Some Model Domains

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