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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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