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Traces and Determinants of Pseudodifferential Operators

Simon Scott

Published in print:
2010
Published Online:
January 2011
ISBN:
9780198568360
eISBN:
9780191594748
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568360.001.0001
Subject:
Mathematics, Analysis

This text provides a broad account of the theory of traces and determinants on geometric algebras of differential and pseudodifferential operators over compact manifolds. Trace and determinant ... More


Geometric Families of Pseudodifferential Operators and Determinant Line Bundles

Simon Scott

in Traces and Determinants of Pseudodifferential Operators

Published in print:
2010
Published Online:
January 2011
ISBN:
9780198568360
eISBN:
9780191594748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568360.003.0006
Subject:
Mathematics, Analysis

The final chapter focuses on applications of trace and determinant structures to geometric families of pseudodifferential operators. This is closely entwined with developments in QFT and string ... More


Stationary phase and microlocal analysis

Christopher D. Sogge

in Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160757
eISBN:
9781400850549
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160757.003.0004
Subject:
Mathematics, Numerical Analysis

This chapter discusses basic techniques from the theory of stationary phase. After giving an overview of the method of stationary phase, the chapter moves on to a discussion of pseudodifferential ... More


Multi-parameter Singular Integrals II: General Theory

Brian Street

in Multi-parameter Singular Integrals. (AM-189)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691162515
eISBN:
9781400852758
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162515.003.0005
Subject:
Mathematics, Analysis

This chapter turns to a general theory which generalizes and unifies all of the examples in the preceding chapters. A main issue is that the first definition from the trichotomy does not generalize ... More


The Calder´on-Zygmund Theory I: Ellipticity

Brian Street

in Multi-parameter Singular Integrals. (AM-189)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691162515
eISBN:
9781400852758
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162515.003.0001
Subject:
Mathematics, Analysis

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful ... More


Improved spectral asymptotics and periodic geodesics

Christopher D. Sogge

in Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160757
eISBN:
9781400850549
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160757.003.0005
Subject:
Mathematics, Numerical Analysis

This chapter proves an improved Weyl formula under the assumption that the set of periodic geodesics for (M,g) has measure zero. It then shows trace estimates associated with shrinking spectral ... More


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