18 research outputs found
On a q-analog of a Sahi result
We obtain a -analog of a well known Sahi result on the joint spectrum of
-invariant differential operators with polynomial
coefficients on the vector space of complex -matrices.Comment: 9 pages, some improvements in exposition have been mad
Maximum modulus principle for "holomorphic functions" on the quantum matrix ball
We describe the Shilov boundary ideal for a q-analog of the algebra of
holomorphic functions on the unit ball in the space of matrices and
show that its -envelope is isomorphic to the -algebra of continuous
functions on the quantum unitary group .Comment: 27 pages,v.3:accepted for publication in Journal Funct.Anal.,
crrected som typos, proof of Lemma 10 changed, a reference added, an
acknowledgement adde
Harmonic Analysis on Quantum Complex Hyperbolic Spaces
In this paper we obtain some results of harmonic analysis on quantum complex
hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami
operator and its radial part. The latter appear to be second order
-difference operator, whose eigenfunctions are related to the
Al-Salam-Chihara polynomials. We prove a Plancherel type theorem for it