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How the μ-deformed Segal-Bargmann space gets two measures

Stephen Bruce Sontz (2010)

Banach Center Publications

This note explains how the two measures used to define the μ-deformed Segal-Bargmann space are natural and essentially unique structures. As is well known, the density with respect to Lebesgue measure of each of these measures involves a Macdonald function. Our primary result is that these densities are the solution of a system of ordinary differential equations which is naturally associated with this theory. We then solve this system and find the known densities as well as a "spurious" solution...

How to define "convex functions" on differentiable manifolds

Stefan Rolewicz (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: 1 . if M is a linear manifold, then (M) contains convex functions, 2 . (·) is invariant under diffeomorphisms, 3 . each f ∈ (M) is differentiable on a dense G δ -set, is investigated.

How to solve an operator equation.

Martin Mathieu (1992)

Publicacions Matemàtiques

This article summarizes a series of lectures delivered at the Mathematics Department of the University of Leipzig, Germany, in April 1991, which were to overview techniques for solving operator equations on C*-algebras connected with methods developed in a Spanish-German research project on "Structure and Applications of C*-Algebras of Quotients" (SACQ). One of the researchers in this project was Professor Pere Menal until his unexpected death this April. To his memory this paper shall be dedicated....

Hull-minimal ideals in the Schwartz algebra of the Heisenberg group

J. Ludwig (1998)

Studia Mathematica

For every closed subset C in the dual space Ĥ n of the Heisenberg group H n we describe via the Fourier transform the elements of the hull-minimal ideal j(C) of the Schwartz algebra S ( H n ) and we show that in general for two closed subsets C 1 , C 2 of Ĥ n the product of j ( C 1 ) and j ( C 2 ) is different from j ( C 1 ∩ C 2 ) .

Hyers-Ulam constants of Hilbert spaces

Taneli Huuskonen, Jussi Väısälä (2002)

Studia Mathematica

The best constant in the Hyers-Ulam theorem on isometric approximation in Hilbert spaces is equal to the Jung constant of the space.

Hyperbolic-like manifolds, geometrical properties and holomorphic mappings

Grzegorz Boryczka, Luis Tovar (1996)

Banach Center Publications

The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance ρ X α ( z 0 , z ) [ ] introduced by Dolbeault and Ławrynowicz (1989) in connection with bordered holomorphic chains of dimension one. Several properties of the related hyperbolic-like manifolds are considered remarking the analogies with and differences from the familiar hyperbolic and Stein manifolds. Likewise several examples are treated in detail.

Hypercyclic and chaotic weighted shifts

K.-G. Grosse-Erdmann (2000)

Studia Mathematica

Extending previous results of H. Salas we obtain a characterisation of hypercyclic weighted shifts on an arbitrary F-sequence space in which the canonical unit vectors ( e n ) form a Schauder basis. If the basis is unconditional we give a characterisation of those hypercyclic weighted shifts that are even chaotic.

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