Problems in Analysis Related to P.D.E., Geometry, and Several Complex Variables

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Abstract DMS-0245242Charles Fefferman and Elias Stein Problems in analysis Among the problems that will be investigated are:(1) The domination of pseudo-differential operators.(2) Singular integrals which have that singularities on flag manifolds, and their application to several complex manifolds.(3) Classification of conformal manifolds analogous to Branson's Q curvature.(4) Estimates for oscillatory integrals and questions of stability.(5) Efficient hedging strategies in the presence of transaction costs. The methods of harmonic analysis and partial differential equations have important applications in many fields of science, for example physics, engineering, and finance; also in different parts of mathematics, for example geometry. The underlying reason is that partial differential equations express the laws which govern a wide variety of phenomena, while harmonic analysis is a central tool to understand the solutions of the equations.