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Displaying similar documents to “An Lp Estimate for the Difference of Derivatives of Spectral Expansions Arising by One-dimensional Schroedinger Operators”

Some remarks on Bochner-Riesz means

S. Thangavelu (2000)

Colloquium Mathematicae

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We study L p norm convergence of Bochner-Riesz means S R δ f associated with certain non-negative differential operators. When the kernel S R m ( x , y ) satisfies a weak estimate for large values of m we prove L p norm convergence of S R δ f for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.

Sturm-Liouville systems are Riesz-spectral systems

Cédric Delattre, Denis Dochain, Joseph Winkin (2003)

International Journal of Applied Mathematics and Computer Science

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The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C_0-semigroup of bounded linear operators.

Continuity versus boundedness of the spectral factorization mapping

Holger Boche, Volker Pohl (2008)

Studia Mathematica

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This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping 𝔖 is continuous or bounded. It is shown that 𝔖 is continuous if and only if the Riesz projection is bounded on the algebra, and that 𝔖 is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, 𝔖 can never be both continuous and bounded, on any algebra under consideration.

Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators

Giancarlo Mauceri (1981)

Annales de l'institut Fourier

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We study the Riesz means for the eigenfunction expansions of a class of hypoelliptic differential operators on the Heisenberg group. The operators we consider are homogeneous with respect to dilations and invariant under the action of the unitary group. We obtain convergence results in L p norm, at Lebesgue points and almost everywhere. We also prove localization results.