Analytic Pseudodifferential Operators for the Heisenberg Group and Local Solvability (eBook)

Daryl Geller (Autor)

eBook Download: PDF

2014
Princeton University Press (Verlag)
978-1-4008-6073-9 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 14.7.2014
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Legacy Library
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Schlagworte: analytic function • Analytic set • associative property • asymptotic expansion • Atkinson's theorem • Banach space • bilinear map • Boundary value problem • bounded function • bounded operator • Bump function • Cauchy problem • Cauchy–Schwarz inequality • Cauchy's Integral Formula • Cayley transform • Characteristic function (probability theory) • Characterization (mathematics) • coefficient • Cokernel • combinatorics • Complex conjugate • Complexification (Lie group) • complex number • Contact Geometry • convolution • CR manifold • C space • Darboux's theorem • Darboux's theorem (analysis) • Diagram (category theory) • diffeomorphism • Difference quotient • Differential operator • Dimension (vector space) • Dirac delta function • Eigenvalues and Eigenvectors • elliptic operator • Equation • existential quantification • Explicit formulae (L-function) • factorial • Fourier inversion theorem • Fourier series • Fourier transform • fundamental solution • Heisenberg group • Hermitian adjoint • hilbert space • Hodge Theory • Hölder's inequality • hypoelliptic operator • implicit function theorem • integral transform • Invertible matrix • Leibniz integral rule • Lie algebra • Mathematical Induction • Mathematical Proof • mean value theorem • multinomial theorem • Neighbourhood (mathematics) • Neumann series • nilpotent group • Orthogonal transformation • Orthonormal basis • Oscillatory integral • Paley–Wiener theorem • Parametrix • Parity (mathematics) • partial differential equation • partition of unity • Plancherel theorem • polynomial • power function • power series • Product rule • Property B • pseudo-differential operator • Pullback (category theory) • quadratic form • Regularity theorem • Riesz transform • Schwartz space • scientific notation • Self-adjoint • Self-adjoint operator • Sesquilinear form • Several Complex Variables • Singular integral • Special case • Summation • Support (mathematics) • symmetrization • Theorem • Topology • Triangle Inequality • unbounded operator • Union (set theory) • unitary transformation • Variable (mathematics)
• ISBN-10: 1-4008-6073-3 / 1400860733
• ISBN-13: 978-1-4008-6073-9 / 9781400860739