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Banach algebras with unique uniform norm II

S. J. Bhatt, H. V. Dedania (2001)

Studia Mathematica

Semisimple commutative Banach algebras 𝓐 admitting exactly one uniform norm (not necessarily complete) are investigated. 𝓐 has this Unique Uniform Norm Property iff the completion U(𝓐) of 𝓐 in the spectral radius r(·) has UUNP and, for any non-zero spectral synthesis ideal ℐ of U(𝓐), ℐ ∩ 𝓐 is non-zero. 𝓐 is regular iff U(𝓐) is regular and, for any spectral synthesis ideal ℐ of 𝓐, 𝓐/ℐ has UUNP iff U(𝓐) is regular and for any spectral synthesis ideal ℐ of U(𝓐), ℐ = k(h(𝓐 ∩ ℐ)) (hulls...

Bellman approach to some problems in harmonic analysis

Alexander Volberg (2001/2002)

Séminaire Équations aux dérivées partielles

The stochastic optimal control uses the differential equation of Bellman and its solution - the Bellman function. Recently the Bellman function proved to be an efficient tool for solving some (sometimes old) problems in harmonic analysis.

Besov spaces and function series on Lie groups

Leszek Skrzypczak (1993)

Commentationes Mathematicae Universitatis Carolinae

In the paper we investigate the absolute convergence in the sup-norm of Harish-Chandra's Fourier series of functions belonging to Besov spaces defined on non-compact connected Lie groups.

Besov spaces and function series on Lie groups (II).

Leszek Skrzypczak (1993)

Collectanea Mathematica

In this paper we investigate the absolute convergence in the sup-norm of two-sided Harish-Chandra's Fourier series of functions belonging to Zygmund-Hölder spaces defined on non-compact connected Lie groups.[Part I of the article in MR1240211].

Besov spaces on symmetric manifolds—the atomic decomposition

Leszek Skrzypczak (1997)

Studia Mathematica

We give the atomic decomposition of the inhomogeneous Besov spaces defined on symmetric Riemannian spaces of noncompact type. As an application we get a theorem of Bernstein type for the Helgason-Fourier transform.

Beurling algebras and uniform norms

S. J. Bhatt, H. V. Dedania (2004)

Studia Mathematica

Given a locally compact abelian group G with a measurable weight ω, it is shown that the Beurling algebra L¹(G,ω) admits either exactly one uniform norm or infinitely many uniform norms, and that L¹(G,ω) admits exactly one uniform norm iff it admits a minimum uniform norm.

Beurling-Figà-Talamanca-Herz algebras

Serap Öztop, Volker Runde, Nico Spronk (2012)

Studia Mathematica

For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras A p ( G , ω ) . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We prove that...

Currently displaying 321 – 340 of 2299