Leseprobe
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Calculus on Heisenberg Manifolds. (AM-119), Volume 119
Richard Beals, Peter Charles Greiner
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
A classic treatment of the hypoelliptic calculus on Heisenberg Manifolds
The classical pseudodifferential calculus is well adapted to detailed study of elliptic operators such as the Laplacian associated to the De Rham complex. This book develops a full asymptotic calculus adapted to certain second order operators which are hypoelliptic but not elliptic. The motivating example is the operator _b associated to the ∂_b-complex on a CR-manifold. Like the Laplacian, _b is a natural operator of intrinsic interest, a prototype of a general class, and a test case. Principal terms of parametrices and other operators associated to _b are calculated on both the symbol side and the kernel side. It is hoped that this viewpoint on pseudodifferential operators will be fruitful in attacking other nonelliptic problems, including more degenerate cases of _b.
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Pointwise product, Structure constants, Identity element, Unit circle, Pseudo-differential operator, Asymptotic expansion, Computation, Approximation, Pointwise, Calculation, Fourier integral operator, De Rham cohomology, Differential operator, Polynomial, Heisenberg group, Invertible matrix, Summation, Estimation, Subset, Theorem, Nilpotent group, Fourier transform, Homogeneous function, Principal part, Complex geometry, Parametrix, Tangent bundle, Partial differential equation, Dimension (vector space), Transpose, Riemannian manifold, Integration by parts, Affine transformation, Adjoint, Manifold, Hilbert space, Self-adjoint, Singular integral, Heat equation, Complex manifold, Smoothing, Codimension, Hypoelliptic operator, Differentiable manifold, Function space, Vector field, Several complex variables, Convolution, Derivative