000			04424nam a22005895i 4500
001			978-0-8176-4995-1
003			DE-He213
005			20251006084440.0
007			cr nn 008mamaa
008			101013s2011 xxu| s |||| 0|eng d
020			_a9780817649951
020			_a99780817649951
024	7		_a10.1007/978-0-8176-4995-1 _2doi
082	0	4	_a515.353 _223
100	1		_aCalin, Ovidiu. _eauthor.
245	1	0	_aHeat Kernels for Elliptic and Sub-elliptic Operators _h[electronic resource] : _bMethods and Techniques / _cby Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki.
250			_a1.
264		1	_aBoston : _bBirkhäuser Boston, _c2011.
300			_aXVIII, 436p. 25 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aApplied and Numerical Harmonic Analysis
505	0		_aPart I. Traditional Methods for Computing Heat Kernels -- Introduction -- Stochastic Analysis Method -- A Brief Introduction to Calculus of Variations -- The Path Integral Approach -- The Geometric Method -- Commuting Operators -- Fourier Transform Method -- The Eigenfunctions Expansion Method -- Part II. Heat Kernel on Nilpotent Lie Groups and Nilmanifolds -- Laplacians and Sub-Laplacians -- Heat Kernels for Laplacians and Step 2 Sub-Laplacians -- Heat Kernel for Sub-Laplacian on the Sphere S^3 -- Part III. Laguerre Calculus and Fourier Method -- Finding Heat Kernels by Using Laguerre Calculus -- Constructing Heat Kernel for Degenerate Elliptic Operators -- Heat Kernel for the Kohn Laplacian on the Heisenberg Group -- Part IV. Pseudo-Differential Operators -- The Psuedo-Differential Operators Technique -- Bibliography -- Index.
520			_aThis 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. The work is divided into four main parts: Part I treats the heat kernel by traditional methods, such as the Fourier transform method, paths integrals, variational calculus, and eigenvalue expansion; Part II deals with the heat kernel on nilpotent Lie groups and nilmanifolds; Part III examines Laguerre calculus applications; Part IV uses the method of pseudo-differential operators to describe heat kernels. Topics and features: •comprehensive treatment from the point of view of distinct branches of mathematics, such as stochastic processes, differential geometry, special functions, quantum mechanics, and PDEs; •novelty of the work is in the diverse methods used to compute heat kernels for elliptic and sub-elliptic operators; •most of the heat kernels computable by means of elementary functions are covered in the work; •self-contained material on stochastic processes and variational methods is included. 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.
650		0	_aMATHEMATICS.
650		0	_aHARMONIC ANALYSIS.
650		0	_aOPERATOR THEORY.
650		0	_aDIFFERENTIAL EQUATIONS, PARTIAL.
650		0	_aGLOBAL DIFFERENTIAL GEOMETRY.
650		0	_aDISTRIBUTION (PROBABILITY THEORY).
650		0	_aMATHEMATICAL PHYSICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aPARTIAL DIFFERENTIAL EQUATIONS.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
650	2	4	_aOPERATOR THEORY.
650	2	4	_aDIFFERENTIAL GEOMETRY.
650	2	4	_aPROBABILITY THEORY AND STOCHASTIC PROCESSES.
650	2	4	_aABSTRACT HARMONIC ANALYSIS.
700	1		_aChang, Der-Chen. _eauthor.
700	1		_aFurutani, Kenro. _eauthor.
700	1		_aIwasaki, Chisato. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817649944
830		0	_aApplied and Numerical Harmonic Analysis
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4995-1 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59841 _d59841