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Heat Kernels for Elliptic and Sub-elliptic Operators - Methods and Techniques (Hardcover, Edition.): Ovidiu Calin, Der-Chen... Heat Kernels for Elliptic and Sub-elliptic Operators - Methods and Techniques (Hardcover, Edition.)
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki
R3,136 Discovery Miles 31 360 Ships in 10 - 15 working days

This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes.
Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.

The Sub-Laplacian Operators of Some Model Domains (Hardcover): Der-Chen Chang, Jingzhi Tie The Sub-Laplacian Operators of Some Model Domains (Hardcover)
Der-Chen Chang, Jingzhi Tie
R4,158 Discovery Miles 41 580 Ships in 12 - 19 working days

The book constructs explicitly the fundamental solution of the sub-Laplacian operator for a family of model domains in Cn+1. This type of domain is a good point-wise model for a Cauchy-Rieman (CR) manifold with diagonalizable Levi form. Qualitative results for such operators have been studied extensively, but exact formulas are difficult to derive. Exact formulas are closely related to the underlying geometry and lead to equations of classical types such as hypergeometric equations and Whittaker's equations.

Geometric Mechanics on Riemannian Manifolds - Applications to Partial Differential Equations (Hardcover, 2005 ed.): Ovidiu... Geometric Mechanics on Riemannian Manifolds - Applications to Partial Differential Equations (Hardcover, 2005 ed.)
Ovidiu Calin, Der-Chen Chang
R2,656 Discovery Miles 26 560 Ships in 10 - 15 working days

* A geometric approach to problems in physics, many of which cannot be solved by any other methods

* Text is enriched with good examples and exercises at the end of every chapter

* Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics

Sub-Riemannian Geometry - General Theory and Examples (Hardcover): Ovidiu Calin, Der-Chen Chang Sub-Riemannian Geometry - General Theory and Examples (Hardcover)
Ovidiu Calin, Der-Chen Chang
R3,987 Discovery Miles 39 870 Ships in 12 - 19 working days

Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples and applications, showing how Heisenberg manifolds (step 2 sub-Riemannian manifolds) might in the future play a role in quantum mechanics similar to the role played by the Riemannian manifolds in classical mechanics. Sub-Riemannian Geometry: General Theory and Examples is the perfect resource for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics interested in the most recent developments in sub-Riemannian geometry.

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