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Semiclassical Microlocal Analysis and Local and Microlocal Semiclassical Asymptotics by Victor Ivrii

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**About this book :- **
**Microlocal Analysis, Sharp Spectral Asymptotics & Applications I ** written by
** Victor Ivrii**.

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory.

In this volume the general microlocal semiclassical approach is developed, and microlocal and local semiclassical spectral asymptotics are derived.

(Victor Ivrii)

**Book Detail :- **
** Title: ** Microlocal Analysis, Sharp Spectral Asymptotics & Applications I
** Edition: **
** Author(s): ** Victor Ivrii
** Publisher: ** Springer International Publishing
** Series: **
** Year: ** 2019
** Pages: ** 938
** Type: ** PDF
** Language: ** English
** ISBN: ** 978-3-030-30556-7,978-3-030-30557-4
** Country: ** Canada
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**About Author :- **

The author ** Victor Ivrii **
is a Soviet, Canadian mathematician who specializes in analysis, microlocal analysis, spectral theory and partial differential equations. He is a professor at the University of Toronto Department of Mathematics. He was an invited speaker at International Congress of Mathematicians, Helsinki—1978 and Berkeley—1986. He graduated from Physical Mathematical School at Novosibirsk State University in 1965, received his University Diploma (equivalent to MSci) in 1970 and PhD in 1973 in Novosibirsk State University. He defended his Doktor nauk thesis in St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences in 1982.

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** • Download PDF Microlocal Analysis, Sharp Spectral Asymptotics & Applications I by Victor Ivrii **

** • Download PDF Microlocal Analysis, Sharp Spectral Asymptotics & Applications II by Victor Ivrii **

** • Download PDF Microlocal Analysis, Sharp Spectral Asymptotics & Applications III by Victor Ivrii **

** • Download PDF Microlocal Analysis, Sharp Spectral Asymptotics & Applications IV by Victor Ivrii **

** • Download PDF Microlocal Analysis, Sharp Spectral Asymptotics & Applications V by Victor Ivrii **

** • Download PDF Precise Spectral Asymptotics for Elliptic Operators by Victor Ivrii **

** • Download PDF Partial Differential Equations by Victor Ivrii **

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**Book Contents :- **
**Microlocal Analysis, Sharp Spectral Asymptotics & Applications I ** written by
** Victor Ivrii**
cover the following topics.
'

Preface

Introduction

Part-I Semiclassical Microlocal Analysis

1. Introduction to Microlocal Analysis

2. Propagation of Singularities in the Interior of the Domain

3. Propagation of Singularities near the Boundary

Part-II Local and Microlocal Semiclassical Spectral Asymptotics in the Interior of the Domain

4. General Theory in the Interior of the Domain

5. Scalar Operators in the Interior of the Domain. Rescaling Technique

6. Operators in the Interior of Domain. Esoteric Theory

Part-III Local and Microlocal Semiclassical Spectral Asymptotics near the Boundary

7. Standard Local Semiclassical Spectral Asymptotics near the Boundary

8. Standard Local Semiclassical Spectral Asymptotics near the Boundary. Miscellaneous

Bibliography

Presentations

Index

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