Analytic Pseudodifferential Operators for the Heisenberg Group and Local Solvability
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A01=Daryl Geller
Analytic function
Analytic set
Associative property
Asymptotic expansion
Atkinson's theorem
Author_Daryl Geller
Banach space
Boundary value problem
Bounded operator
Bump function
Category=PBF
Category=PBKQ
Cauchy problem
Cauchy's integral formula
Cauchy–Schwarz inequality
Characteristic function (probability theory)
Characterization (mathematics)
Combinatorics
Complexification (Lie group)
Contact geometry
Convolution
Darboux's theorem
Darboux's theorem (analysis)
Diagram (category theory)
Difference quotient
Differential operator
Dimension (vector space)
Dirac delta function
Eigenvalues and eigenvectors
Elliptic operator
eq_isMigrated=1
eq_nobargain
Equation
Existential quantification
Explicit formulae (L-function)
Fourier inversion theorem
Fourier transform
Fundamental solution
Heisenberg group
Hilbert space
Hypoelliptic operator
Hölder's inequality
Implicit function theorem
Integral transform
Invertible matrix
Leibniz integral rule
Lie algebra
Mathematical induction
Mean value theorem
Multinomial theorem
Neighbourhood (mathematics)
Orthonormal basis
Oscillatory integral
Paley–Wiener theorem
Parametrix
Parity (mathematics)
Partial differential equation
Plancherel theorem
Polynomial
Pseudo-differential operator
Pullback (category theory)
Regularity theorem
Riesz transform
Schwartz space
Self-adjoint
Self-adjoint operator
Sesquilinear form
Singular integral
Special case
Summation
Support (mathematics)
Symmetrization
Theorem
Triangle inequality
Variable (mathematics)
Product details
- ISBN 9780691608297
- Weight: 851g
- Dimensions: 178 x 254mm
- Publication Date: 14 Jul 2014
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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Many of the operators one meets in several complex variables, such as the famous Lewy operator, are not locally solvable. Nevertheless, such an operator L can be thoroughly studied if one can find a suitable relative parametrix--an operator K such that LK is essentially the orthogonal projection onto the range of L. The analysis is by far most decisive if one is able to work in the real analytic, as opposed to the smooth, setting. With this motivation, the author develops an analytic calculus for the Heisenberg group. Features include: simple, explicit formulae for products and adjoints; simple representation-theoretic conditions, analogous to ellipticity, for finding parametrices in the calculus; invariance under analytic contact transformations; regularity with respect to non-isotropic Sobolev and Lipschitz spaces; and preservation of local analyticity. The calculus is suitable for doing analysis on real analytic strictly pseudoconvex CR manifolds. In this context, the main new application is a proof that the Szego projection preserves local analyticity, even in the three-dimensional setting.
Relative analytic parametrices are also constructed for the adjoint of the tangential Cauchy-Riemann operator. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
