Oscillating Multipliers and Bochner-Riesz Means.

Date of Submission

February 2011

Date of Award

2-28-2012

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Mathematics

Department

Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)

Supervisor

Thangavelu, S. (TSMU-Bangalore; ISI)

Abstract (Summary of the Work)

Suppose P is a differential operator of degree d on a Riemannian manifold M, which is self adjoint and forınally non-negative. LetPf = AdBbe the spectral resolution of P. Given a houmled functian m(A) we can define the operator in(P) by00 m(P) = m( )dE.Such operators are always bounded on L(M). However, some smoothness assumptions are Imeedad on m(A) to ensure that m(P) : LP(M) + P(M) is bounded for p # 2. IL is a basic problem in Harmonic Analysis to find sufficient conditions on m so the the operator n(P) will be bounded on IP(M). There is a universal multiplier theorem due to Slein (36], which guarantees that m(P) is bounded on LP (M), 1

Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843402

Control Number

ISILib-TH

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

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