Displaying similar documents to “Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators”

Some remarks on Bochner-Riesz means

S. Thangavelu (2000)

Colloquium Mathematicae

Similarity:

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.

A microlocal F. and M. Riesz theorem with applications.

Raymondus G. M. Brummelhuis (1989)

Revista Matemática Iberoamericana

Similarity:

Consider, by way of example, the following F. and M. Riesz theorem for R: Let μ be a finite measure on R whose Fourier transform μ* is supported in a closed convex cone which is proper, that is, which contains no entire line. Then μ is absolutely continuous (cf. Stein and Weiss [SW]). Here, as in the sequel, absolutely continuous means with respect to Lebesque measure. In this theorem one can replace the condition on the support of μ* by a similar condition on the wave front set WF(μ)...

Compact AC-operators

Ian Doust, Byron Walden (1996)

Studia Mathematica

Similarity:

We prove that compact AC-operators have a representation as a combination of disjoint projections which mirrors that for compact normal operators. We also show that unlike arbitrary AC-operators, compact AC-operators admit a unique splitting into real and imaginary parts, and that these parts must necessarily be compact.

Heat kernels and Riesz transforms on nilpotent Lie groups

A. ter Elst, Derek Robinson, Adam Sikora (1998)

Colloquium Mathematicae

Similarity:

We consider pure mth order subcoercive operators with complex coefficients acting on a connected nilpotent Lie group. We derive Gaussian bounds with the correct small time singularity and the optimal large time asymptotic behaviour on the heat kernel and all its derivatives, both right and left. Further we prove that the Riesz transforms of all orders are bounded on the Lp -spaces with p ∈ (1, ∞). Finally, for second-order operators with real coefficients we derive matching Gaussian...

A restriction theorem for the Heisenberg motion

P. Ratnakumar, Rama Rawat, S. Thangavelu (1997)

Studia Mathematica

Similarity:

We prove a restriction theorem for the class-1 representations of the Heisenberg motion group. This is done using an improvement of the restriction theorem for the special Hermite projection operators proved in [13]. We also prove a restriction theorem for the Heisenberg group.