Search results for "Convolution operator"

showing 2 items of 2 documents

Functional calculi for convolution operators on a discrete, periodic, solvable group

2009

Suppose T is a bounded self-adjoint operator on the Hilbert space L2(X,μ) and let T=∫SpL2TλdE(λ) be its spectral resolution. Let F be a Borel bounded function on [−a,a], SpL2T⊂[−a,a]. We say that F is a spectral Lp-multiplier for T, if F(T)=∫SpL2TF(λ)dE(λ) is a bounded operator on Lp(X,μ). The paper deals with l1-multipliers, where X=G is a discrete (countable) solvable group with ∀x∈G, x4=1, μ is the counting measure and TΦ:l2(G)∋ξ↦ξ∗Φ∈l2(G), where Φ=Φ∗ is a l1(G) function, suppΦ generates G. The main result of the paper states that there exists a Ψ on G such that all l1-multipliers for TΨ are real analytic at every interior point of Spl2(G)TΨ. We also exhibit self-adjoint Φ′s in l1(G) suc…

Discrete mathematicsDiscrete groupDiscrete groupHilbert spacel1-multipliersFunction (mathematics)ConvolutionBounded operatorFunctional calculiCombinatoricssymbols.namesakeCounting measureSolvable groupBounded functionsymbolsConvolution operatorAnalysisMathematicsJournal of Functional Analysis
researchProduct

Beurling ultradistributions of Lp-growth

2003

We study the convolutors and the surjective convolution operators acting on spaces of ultradistributions of Lp-growth. In the case p = 2 we obtain complete characterizations. Some results on hypoellipticity are also included.  2003 Elsevier Science (USA). All rights reserved.

UltradistributionsPure mathematicsFunctional analysisApplied MathematicsConvolution operatorsMathematical analysisConvolutionSurjective functionsymbols.namesakeFourier transformConvolutorssymbolsConvolution equationAnalysisMathematicsJournal of Mathematical Analysis and Applications
researchProduct