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Rough estimates on the scalar heat kernel

Jean-Michel Bismut

in Hypoelliptic Laplacian and Orbital Integrals (AM-177)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691151298
eISBN:
9781400840571
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151298.003.0013
Subject:
Mathematics, Geometry / Topology

This chapter establishes rough estimates on the heat kernel rb,tX for the scalar hypoelliptic operator AbX on X defined in the preceding chapter. By rough estimates, this chapter refers to just the ... More


Refined estimates on the scalar heat kernel for bounded b

Jean-Michel Bismut

in Hypoelliptic Laplacian and Orbital Integrals (AM-177)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691151298
eISBN:
9781400840571
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151298.003.0014
Subject:
Mathematics, Geometry / Topology

This chapter obtains uniform bounds for the kernels rb,tX and another rb,tX for bounded b > 0, with the proper decay at infinity on X or ̂X. These bounds will be used to obtain corresponding bounds ... More


Improved Estimates by Means of Airy-Type Analysis

Isroil A. Ikromov and Detlef Müller

in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170541
eISBN:
9781400881246
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170541.003.0005
Subject:
Mathematics, Geometry / Topology

This chapter turns to the proof of a proposition from the previous chapter. Given the operators appearing in that proposition, this chapter establishes the endpoint result thereof by means of Stein's ... More


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