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A triple ratio on the Silov boundary of a bounded symmetric domain

Jean-Louis Clerc (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let D be a Hermitian symmetric space of tube type, S its Silov boundary and G the neutral component of the group of bi-holomorphic diffeomorphisms of D . Our main interest is in studying the action of G on S 3 = S × S × S . Sections 1 and 2 are part of a joint work with B. Ørsted (see [4]). In Section 1, as a pedagogical introduction, we study the case where D is the unit disc and S is the circle. This is a fairly elementary and explicit case, where one can easily get a flavour of the more general results. In Section...

Harmonic functions on classical rank one balls

Philippe Jaming (2001)

Bollettino dell'Unione Matematica Italiana

In questo articolo studieremo le relazioni fra le funzioni armoniche nella palla iperbolica (sia essa reale, complessa o quaternionica), le funzione armoniche euclidee in questa palla, e le funzione pluriarmoniche sotto certe condizioni di crescita. In particolare, estenderemo al caso quaternionico risultati anteriori dell'autore (nel caso reale), e di A. Bonami, J. Bruna e S. Grellier (nel caso complesso).

On the Toëplitz corona problem.

Eric Amar (2003)

Publicacions Matemàtiques

The aim of this note is to characterize the vectors g = (g1, . . . ,gk) of bounded holomorphic functions in the unit ball or in the unit polydisk of Cn such that the Corona is true for them in terms of the H2 Corona for measures on the boundary.

Structure of the kernel of higher spin Dirac operators

Martin Plechšmíd (2001)

Commentationes Mathematicae Universitatis Carolinae

Polynomials on n with values in an irreducible Spin n -module form a natural representation space for the group Spin n . These representations are completely reducible. In the paper, we give a complete description of their decompositions into irreducible components for polynomials with values in a certain range of irreducible modules. The results are used to describe the structure of kernels of conformally invariant elliptic first order systems acting on maps on n with values in these modules.

The Hua system on irreducible Hermitian symmetric spaces of nontube type

Dariusz Buraczewski (2004)

Annales de l’institut Fourier

Let G / K be an irreducible Hermitian symmetric space of noncompact type. We study a G - invariant system of differential operators on G / K called the Hua system. It was proved by K. Johnson and A. Korányi that if G / K is a Hermitian symmetric space of tube type, then the space of Poisson-Szegö integrals is precisely the space of zeros of the Hua system. N. Berline and M. Vergne raised the question about the nature of the common solutions of the Hua system for Hermitian symmetric spaces of nontube type. In...

Twisted spherical means in annular regions in n and support theorems

Rama Rawat, R.K. Srivastava (2009)

Annales de l’institut Fourier

Let Z ( Ann ( r , R ) ) be the class of all continuous functions f on the annulus Ann ( r , R ) in n with twisted spherical mean f × μ s ( z ) = 0 , whenever z n and s > 0 satisfy the condition that the sphere S s ( z ) Ann ( r , R ) and ball B r ( 0 ) B s ( z ) . In this paper, we give a characterization for functions in Z ( Ann ( r , R ) ) in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in n which improve some of the earlier results.

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