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.
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Автор: Marco Bramanti, Luca Brandolini, Maria Manfredini, Marco Pedroni Название: Fundamental Solutions and Local Solvability for Nonsmooth Hormander`s Operators ISBN: 1470425599 ISBN-13(EAN): 9781470425593 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 74850.00 T Наличие на складе: Невозможна поставка. Описание: The authors consider operators of the form $L=\sum_{i=1}^{n}X_{i}^{2}+X_{0}$ in a bounded domain of $\mathbb{R}^{p}$ where $X_{0},X_{1},\ldots,X_{n}$ are nonsmooth Hormander`s vector fields of step $r$ such that the highest order commutators are only Holder continuous.
Автор: Pierluigi Colli; Angelo Favini; Elisabetta Rocca; Название: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs ISBN: 3319644882 ISBN-13(EAN): 9783319644882 Издательство: Springer Рейтинг: Цена: 121110.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics.
Автор: Colli Pierluigi, Favini Angelo, Rocca Elisabetta Название: Solvability, Regularity, and Optimal Control of Boundary Value Problems for Pdes: In Honour of Prof. Gianni Gilardi ISBN: 3319878042 ISBN-13(EAN): 9783319878041 Издательство: Springer Рейтинг: Цена: 121110.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics.
Автор: J?rgen Berndt; Franco Tricerri; Lieven Vanhecke Название: Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces ISBN: 3540590013 ISBN-13(EAN): 9783540590019 Издательство: Springer Рейтинг: Цена: 23250.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Generalized Heisenberg groups and Damek-Ricci harmonic spaces are both Lie groups with a number of properties and applications. This study explores their Riemannian geometry by means of a detailed treatment of their Jacobi vector fields and Jacobi operators.
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