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Convolution operators on the dual of hypergroup algebras

Ali Ghaffari (2003)

Commentationes Mathematicae Universitatis Carolinae

Let X be a hypergroup. In this paper, we define a locally convex topology β on L ( X ) such that ( L ( X ) , β ) * with the strong topology can be identified with a Banach subspace of L ( X ) * . We prove that if X has a Haar measure, then the dual to this subspace is L C ( X ) * * = cl { F ∈ L ( X ) * * ; F has compact carrier}. Moreover, we study the operators on L ( X ) * and L 0 ∞ ( X ) which commute with translations and convolutions. We prove, among other things, that if wap ( L ( X ) ) is left stationary, then there is a weakly compact operator T on L ( X ) * which commutes with convolutions if and...

Convolution Products in L1(R+), Integral Transforms and Fractional Calculus

Miana, Pedro (2005)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 43A20, 26A33 (main), 44A10, 44A15We prove equalities in the Banach algebra L1(R+). We apply them to integral transforms and fractional calculus.* Partially supported by Project BFM2001-1793 of the MCYT-DGI and FEDER and Project E-12/25 of D.G.A.

Convolution-dominated integral operators

Gero Fendler, Karlheinz Gröchenig, Michael Leinert (2010)

Banach Center Publications

For a locally compact group G we consider the algebra CD(G) of convolution-dominated operators on L²(G), where an operator A: L²(G) → L²(G) is called convolution-dominated if there exists a ∈ L¹(G) such that for all f ∈ L²(G) |Af(x)| ≤ a⋆|f|(x), for almost all x ∈ G. (1) The case of discrete groups was treated in previous publications [fgl08a, fgl08]. For non-discrete groups we investigate a subalgebra of regular convolution-dominated operators generated by product convolution operators, where the...

Convolutions on compact groups and Fourier algebras of coset spaces

Brian E. Forrest, Ebrahim Samei, Nico Spronk (2010)

Studia Mathematica

We study two related questions. (1) For a compact group G, what are the ranges of the convolution maps on A(G × G) given for u,v in A(G) by u × v ↦ u*v̌ (v̌(s) = v(s^-1)) and u × v ↦ u*v? (2) For a locally compact group G and a compact subgroup K, what are the amenability properties of the Fourier algebra of the coset space A(G/K)? The algebra A(G/K) was defined and studied by the first named author. In answering the first question, we obtain, for compact groups which do not...

Corrigenda: On the product theory of singular integrals.

Alexander Nagel, Elias M. Stein (2005)

Revista Matemática Iberoamericana

We wish to acknowledge and correct an error in a proof in our paper On the product theory of singular integrals, which appeared in Revista Matemática Iberoamericana, volume 20, number 2, 2004, pages 531-561.

Currently displaying 121 – 140 of 151