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Let $H_{n}$ be the Heisenberg group of dimension $2 n + 1$ . Let $L_{1}, \dots, L_{n}$ be the partial sub-Laplacians on $H_{n}$ and $T$ the central element of the Lie algebra of $H_{n}$ . We prove that the kernel of the operator $m (L_{1}, \dots, L_{n}, - i T)$ is in the Schwartz space $S (H_{n})$ if $m \in S (R^{n + 1})$ . We prove also that the kernel of the operator $h (L_{1}, \dots, L_{n})$ is in $S (H_{n})$ if $h \in S (R^{n})$ and that the kernel of the operator $g (L, - i T)$ is in $S (H_{n})$ if $g \in S (R^{2})$ . Here $L = L_{1} + \dots + L_{n}$ is the Kohn-Laplacian on $H_{n}$ .

Schwartz spaces associated with some non-differential convolution operators on homogeneous groups

Jacek Dziubański (1992)

Colloquium Mathematicae

Second degree polynomials and the fundamental theorems of harmonic analysis.

McKennon, Kelly (1982)

International Journal of Mathematics and Mathematical Sciences

Second duals of measure algebras [Book]

H. G. Dales, A. T.-M. Lau, D. Strauss (2011)

Sections induced from weakly sequentially complete spaces

Charles Dunkl, Donald Ramirez (1973)

Studia Mathematica

Segal Algebras with Functorial Properties.

Viktor Losert (1983)

Monatshefte für Mathematik

Selberg Type Zeta Functions for the Group of Complex Two by Two Matrices of Determinant One.

David Scott (1980)

Mathematische Annalen

Selberg's trace formula on the $k$ -regular tree and applications.

Terras, Audrey, Wallace, Dorothy (2003)

International Journal of Mathematics and Mathematical Sciences

Self-affine measures that are $L^{p}$ -improving

Kathryn E. Hare (2015)

Colloquium Mathematicae

A measure is called $L^{p}$ -improving if it acts by convolution as a bounded operator from $L^{q}$ to L² for some q < 2. Interesting examples include Riesz product measures, Cantor measures and certain measures on curves. We show that equicontractive, self-similar measures are $L^{p}$ -improving if and only if they satisfy a suitable linear independence property. Certain self-affine measures are also seen to be $L^{p}$ -improving.

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Displaying 1 – 20 of 242

Sampling of Band-Limited Vectors.

Sampling of Paley-Wiener Functions on Stratified Groups.

Saturation auf kompakten Gruppen und kompakten symmetrischen Räumen.

Saturation on Locally Compact Abelian Groups.

Saturation on Locally Compact Abelian Groups: An Extended Theorem.

Scalar irreducibility of Eigenspace Representations associated to a symmetric space.

Schwartz kernels on the Heisenberg group

Schwartz spaces associated with some non-differential convolution operators on homogeneous groups

Second degree polynomials and the fundamental theorems of harmonic analysis.

Second duals of measure algebras [Book]

Sections induced from weakly sequentially complete spaces

Segal Algebras with Functorial Properties.

Selberg Type Zeta Functions for the Group of Complex Two by Two Matrices of Determinant One.

Selberg's trace formula on the $k$ -regular tree and applications.

Self-affine measures that are $L^{p}$ -improving

Semicharacters and Solvable Lie Croups.

Semigroup actions on homogeneous spaces.

Semigroup algebras having regular multiplication

Semigroup compactifications by generalized distal functions and a fixed point theorem.

Semigroupes de contractions linéaires sur C(X) : irrédductibilité et théorèmes de convergence.

Currently displaying 1 – 20 of 242