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Harmonic analysis. Fourier analysis --- Harmonic functions --- 517.57 --- Functions, Harmonic --- Laplace's equations --- Bessel functions --- Differential equations, Partial --- Fourier series --- Harmonic analysis --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions --- Harmonic functions. --- 517.57 Harmonic functions and their generalizations. Subharmonic functions. Polyharmonic functions. Plurisubharmonic functions

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This comprehensive monograph is ideal for established researchers in the field and also graduate students who wish to learn more about the subject. The text is made accessible to a broad audience as it does not require any knowledge of Lie groups and only a limited knowledge of differential geometry. The author's primary emphasis is on potential theory on the hyperbolic ball, but many other relevant results for the hyperbolic upper half-space are included both in the text and in the end-of-chapter exercises. These exercises expand on the topics covered in the chapter and involve routine computations and inequalities not included in the text. The book also includes some open problems, which may be a source for potential research projects.

Harmonic functions. --- Subharmonic functions. --- Hyperbolic spaces. --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean --- Functions, Subharmonic --- Functions of real variables --- Potential theory (Mathematics) --- Functions, Harmonic --- Laplace's equations --- Bessel functions --- Differential equations, Partial --- Fourier series --- Harmonic analysis --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics

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No detailed description available for "Analyticity in Infinite Dimensional Spaces".

Variétés (mathématiques) --- Applications holomorphes. --- Manifolds (Mathematics) --- Holomorphic mappings. --- Analytic functions. --- Harmonic functions. --- Analytic mappings. --- Mappings, Analytic --- Functions of several complex variables --- Mappings (Mathematics) --- Functions, Harmonic --- Laplace's equations --- Bessel functions --- Differential equations, Partial --- Fourier series --- Harmonic analysis --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's --- Plurisubharmonic functions --- Fonctions de plusieurs variables complexes --- Fonctions plurisousharmoniques --- Functions of several complex variables. --- Variétés (mathématiques) --- Applications holomorphes --- Fonctions analytiques

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Analytic functions --- Approximation theory --- Harmonic functions --- Linear operators --- Spectral theory (Mathematics) --- 517.5 --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Functions, Harmonic --- Laplace's equations --- Bessel functions --- Differential equations, Partial --- Fourier series --- Harmonic analysis --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's --- 517.5 Theory of functions --- Theory of functions

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The existence, for every sub-Laplacian, of a homogeneous fundamental solution smooth out of the origin, plays a crucial role in the book. This makes it possible to develop an exhaustive Potential Theory, almost completely parallel to that of the classical Laplace operator. This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. In recent years, sub-Laplacian operators have received considerable attention due to their special role in the theory of linear second-order PDE's with semidefinite characteristic form. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra nor in differential geometry. It is thus addressed, besides PhD students, to junior and senior researchers in different areas such as: partial differential equations; geometric control theory; geometric measure theory and minimal surfaces in stratified Lie groups.

Potential theory (Mathematics) --- Harmonic functions. --- Laplacian operator. --- Lie groups. --- Differential equations, Partial. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Partial differential equations --- Operator, Laplacian --- Differential equations, Partial --- Functions, Harmonic --- Laplace's equations --- Bessel functions --- Fourier series --- Harmonic analysis --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Algebra. --- Differential equations, partial. --- Potential theory (Mathematics). --- Topological Groups. --- Partial Differential Equations. --- Potential Theory. --- Topological Groups, Lie Groups. --- Groups, Topological --- Continuous groups --- Mathematics --- Partial differential equations. --- Topological groups.