Solution of the Dirichlet Problem in simply connected domains. The case of real analytic boundary. The transformation law for the Szego kernel under conformal mappings. The Ahlfors map of a multiply connected domain. The Dirichlet problem in multiply connected domains. The Bergman kernel and the Szego kernel. Zeroes of the Szego kernel. Local boundary behavior of holomorphic mappings.
The Greens function and the Bergman kernel. Bergman kernel function at boundary points of certain domains in C", Math. In particular, explicit relationships to generalized variants of the Riemann zeta function and Dirichlet L-series are established and a concept of hypercomplex multiplication of lattices is introduced.
Applications to the theory of Hilbert spaces with reproducing kernels, to partial differential equations and index theory on some conformal manifolds are also described. The following ISBNs are associated with this title:.
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Separate different tags with a comma. To include a comma in your tag, surround the tag with double quotes. Please enable cookies in your browser to get the full Trove experience. Skip to content Skip to search. Language English View all editions Prev Next edition 3 of 3. Series Frontiers in mathematics Subjects Automorphic forms.
Generalized analytic automorphic forms in hypercomplex spaces
Functions of complex variables. Hardy spaces. Summary "The aim of this book is to provide a first comprehensive overview of the basic theory of hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces.
It gives a summary on the research results obtained over the last five years and establishes a new field within the theory of functions of hypercomplex variables and within analytic number theory. Vector- and Clifford algebra-valued Eisenstein and Poincare series are constructed within this framework and a detailed description of their analytic and number theoretical properties is provided. In particular, explicit relationships to higher dimensional vector valued variants of the Riemann zeta function and Dirichlet series are established and a concept of hypercomplex multiplication of lattices is introduced.
Applications to the theory of Hilbert spaces with reproducing kernels, to partial differential equations and index theory on some conformally flat manifolds are also included.