Wyniki wyszukiwania

1

A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)

100%

Godoy T., Saal L.

Colloquium Mathematicum

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2006

|

tom 106

|

nr 2

231-255

EN

Let 𝓢(Hₙ) be the space of Schwartz functions on the Heisenberg group Hₙ. We define a spherical transform on 𝓢(Hₙ) associated to the action (by automorphisms) of U(p,q) on Hₙ, p + q = n. We determine its kernel and image and obtain an inversion formula analogous to the Godement-Plancherel formula.

2

On the relative fundamental solutions for a second order differential operator on the Heisenberg group

100%

Godoy T., Saal L.

Studia Mathematica

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2001

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tom 145

|

nr 2

143-164

EN

Let Hₙ be the (2n+1)-dimensional Heisenberg group, let p,q ≥ 1 be integers satisfying p+q=n, and let $L = ∑_{j=1}^{p} (X²_{j} + Y²_{j}) -∑_{j=p+1}^{n} (X²_{j} + Y²_{j})$, where {X₁,Y₁,...,Xₙ,Yₙ,T} denotes the standard basis of the Lie algebra of Hₙ. We compute explicitly a relative fundamental solution for L.

3

Some spectral results on $L^{2}(H_{n})$ related to the action of U(p,q)

100%

Godoy T., Saal L.

Colloquium Mathematicum

|

2000

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tom 86

|

nr 2

177-187

EN

Let $H_{n}$ be the (2n+1)-dimensional Heisenberg group, let p,q be two non-negative integers satisfying p+q=n and let G be the semidirect product of U(p,q) and $H_{n}$. So $L^{2}(H_{n})$ has a natural structure of G-module. We obtain a decomposition of $L^{2}(H_{n})$ as a direct integral of irreducible representations of G. On the other hand, we give an explicit description of the joint spectrum σ(L,iT) in $L^{2}(H_{n})$ where $L=\sum_{j=1}^{p} (X_{j}^{2}+Y_{j}^{2}) - \sum_{j=p+1}^{n} (X_{j}^{2}+Y_{j}^{2})$, and where ${X_{1},Y_{1},...,X_{n},Y_{n},T}$ denotes the standard basis of the Lie algebra of $H_{n}$. Finally, we obtain a spectral characterization of the bounded operators on $L^{2}(H_{n})$ that commute with the action of G.

4

On some singular integral operatorsclose to the Hilbert transform

81%

Godoy T., Saal L., Urciuolo M.

Colloquium Mathematicum

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1997

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tom 72

|

nr 1

9-17

EN

Let m: ℝ → ℝ be a function of bounded variation. We prove the $L^p(ℝ)$-boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by $T_m f(x) = p.v. \int k(x-y) m(x+y) f(y)dy$ where $k(x) = \sum_{j ∈ ℤ} 2^j φ _j (2^j x)$ for a family of functions ${φ_j}_{j∈ℤ}$ satisfying conditions (1.1)-(1.3) given below.

Ograniczanie wyników

3 Colloquium Mathematicum

1 Studia Mathematica

4 Godoy T.

4 Saal L.

1 Urciuolo M.

1 2006

1 2001

1 2000

1 1997

A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)

On the relative fundamental solutions for a second order differential operator on the Heisenberg group

Some spectral results on $L^{2}(H_{n})$ related to the action of U(p,q)

On some singular integral operatorsclose to the Hilbert transform