We study a parameterized family of Toeplitz-type operators with respect to specific wavelets whose Fourier transforms are related to Laguerre polynomials. On the one hand, this choice of wavelets underlines the fact that these operators acting on wavelet subspaces share many properties with the classical Toeplitz operators acting on the Bergman spaces. On the other hand, it enables to study poly-Bergman spaces and Toeplitz operators acting on them from a different perspective. Restricting to symbols depending only on vertical variable in the upper half-plane of the complex plane these operators are unitarily equivalent to a multiplication operator with a certain function. Since this function is responsible for many interesting features of these Toeplitz-type operators and their algebras, we investigate its behavior in more detail. As a by-product we obtain an interesting observation about the asymptotic behavior of true poly-analytic Bergman spaces. Isomorphisms between the Calderón-Toeplitz operator algebras and functional algebras are described and their consequences in time-frequency analysis and applications are discussed.Mathematics Subject Classification (2010). Primary 47B35, 42C40; Secondary 47G30, 47L80.

Let G be the "ax + b"-group with the left invariant Haar measure dν and ψ be a fixed real-valued admissible wavelet on L2(R). The structure of the space of Calderón (wavelet) transforms W ψ (L2(R)) inside L2(G, dν) is described. Using this result some representations, properties and the Wick calculus of the Calderón-Toeplitz operators Ta acting on W ψ (L2(R)) whose symbols a = a(ζ) depend on v = ζ for ζ ∈ G are investigated. (2000). Primary 46E22, 47B35; Secondary 42C40. Mathematics Subject Classification

No abstract

No abstract

A Lebesgue-type integration theory in complete bornological locally convex topological vector spaces was introduced by the first author in [17]. In this paper we continue developing this integration technique and formulate and prove some theorems on integrable functions as well as some convergence theorems. An example of Dobrakov integral in non-metrizable complete bornological locally convex spaces is given. (2010). Primary 46G10, Secondary 28B05. Mathematics Subject Classification

No abstract

In this paper we study a generalization of a submeasure notion which is related to a probabilistic concept, especially to Menger spaces where triangular norms play a crucial role. The resulting notion of a τ T -submeasure is suitable for modeling those situations in which we have only probabilistic information about the measure of the set. We characterize a class of universal τ T -submeasures (i.e., τ T -submeasures for an arbitrary t-norm T ) and give explicit formulas for τ T -submeasures for some classes of t-norms. Also, transformations and aggregations of τ T -submeasures are discussed.

No abstract