Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 9

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

An analogue of Hardy's theorem for the Heisenberg group

100%
Thangavelu S.
Colloquium Mathematicum
|
2001
|
tom 87
|
nr 1
137-145
EN
We observe that the classical theorem of Hardy on Fourier transform pairs can be reformulated in terms of the heat kernel associated with the Laplacian on the Euclidean space. This leads to an interesting version of Hardy's theorem for the sublaplacian on the Heisenberg group. We also consider certain Rockland operators on the Heisenberg group and Schrödinger operators on ℝⁿ related to them.
2
Content available remote

On conjugate Poisson integrals and Riesz transforms for the Hermite expansions

100%
Thangavelu S.
Colloquium Mathematicum
|
1993
|
tom 64
|
nr 1
103-113
3
Content available remote

Some remarks on Bochner-Riesz means

100%
Thangavelu S.
Colloquium Mathematicum
|
2000
|
tom 83
|
nr 2
217-230
EN
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.
4
Content available remote

An analogue of Gutzmer's formula for Hermite expansions

100%
Thangavelu S.
Studia Mathematica
|
2008
|
tom 185
|
nr 3
279-290
EN
We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of L²(ℝⁿ) under the Hermite semigroup. We also obtain some new orthogonality relations for complexified Hermite functions.
5
Content available remote

Hardy's theorem for the helgason Fourier transform on noncompact rank one symmetric spaces

100%
Thangavelu S.
Colloquium Mathematicum
|
2002
|
tom 94
|
nr 2
263-280
EN
Let G be a semisimple Lie group with Iwasawa decomposition G = KAN. Let X = G/K be the associated symmetric space and assume that X is of rank one. Let M be the centraliser of A in K and consider an orthonormal basis ${Y_{δ,j}: δ ∈ K̂₀, 1 ≤ j ≤ d_{δ}}$ of L²(K/M) consisting of K-finite functions of type δ on K/M. For a function f on X let f̃(λ,b), λ ∈ ℂ, be the Helgason Fourier transform. Let $h_{t}$ be the heat kernel associated to the Laplace-Beltrami operator and let $Q_{δ}(iλ + ϱ)$ be the Kostant polynomials. We establish the following version of Hardy's theorem for the Helgason Fourier transform: Let f be a function on G/K which satisfies $|f(ka_{r})| ≤ Ch_{t}(r)$. Further assume that for every δ and j the functions $F_{δ,j}(λ) = Q_{δ}(iλ +ϱ)^{-1} ∫_{K/M} f̃(λ,b)Y_{δ,j}(b)db$ satisfy the estimates $|F_{δ,j}(λ)| ≤ C_{δ,j}e^{-tλ²}$ for λ ∈ ℝ. Then f is a constant multiple of the heat kernel $h_{t}$.
6
Content available remote

Oscillating multipliers on the Heisenberg group

64%
Narayanan E., Thangavelu S.
Colloquium Mathematicum
|
2001
|
tom 90
|
nr 1
37-50
EN
Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator $ℒ^{-1/2} sin√ℒ$ is bounded on $L^{p}(Hⁿ)$ for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on $L^{p}$ in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.
7
Content available remote

A restriction theorem for the Heisenberg motion

51%
Ratnakumar P. K., Rawat R., Thangavelu S.
Studia Mathematica
|
1997
|
tom 126
|
nr 1
1-12
EN
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.
8
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

On almost everywhere and mean convergence of Hermite and Laguerre expansions

51%
Thangavelu S.
Colloquium Mathematicum
|
1990
|
tom 60-61
|
nr 1
21-34
9
Content available remote

Some restriction theorems for the Heisenberg group

32%
Thangavelu S.
Studia Mathematica
|
1991
|
tom 99
|
nr 1
1-10
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.