Wyniki wyszukiwania

1

A Wiener type theorem for (U(p,q),Hₙ)

100%

Saal L.

Colloquium Mathematicum

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2010

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tom 119

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nr 2

169-180

EN

It is well known that (U(p,q),Hₙ) is a generalized Gelfand pair. Applying the associated spectral analysis, we prove a theorem of Wiener Tauberian type for the reduced Heisenberg group, which generalizes a known result for the case p = n, q = 0.

2

Explicit fundamental solutions of some second order differential operators on Heisenberg groups

63%

Cardoso I., Saal L.

Colloquium Mathematicum

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2012

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tom 129

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nr 2

263-288

EN

Let p,q,n be natural numbers such that p+q = n. Let 𝔽 be either ℂ, the complex numbers field, or ℍ, the quaternionic division algebra. We consider the Heisenberg group N(p,q,𝔽) defined 𝔽ⁿ × ℑ𝔪 𝔽, with group law given by (v,ζ)(v',ζ') = (v + v', ζ + ζ'- 1/2 ℑ𝔪 B(v,v')), where $B(v,w) = ∑_{j=1}^{p} v_{j}\overline{w_{j}} - ∑_{j=p+1}^{n} v_{j}\overline{w_{j}}$. Let U(p,q,𝔽) be the group of n × n matrices with coefficients in 𝔽 that leave the form B invariant. We compute explicit fundamental solutions of some second order differential operators on N(p,q,𝔽) which are canonically associated to the action of U(p,q,𝔽).

3

The Wigner semi-circle law and the Heisenberg group

63%

Faraut J., Saal L.

Banach Center Publications

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2007

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tom 78

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nr 1

133-143

EN

The Wigner Theorem states that the statistical distribution of the eigenvalues of a random Hermitian matrix converges to the semi-circular law as the dimension goes to infinity. It is possible to establish this result by using harmonic analysis on the Heisenberg group. In fact this convergence corresponds to the topology of the set of spherical functions associated to the action of the unitary group on the Heisenberg group.

Ograniczanie wyników

2 Colloquium Mathematicum

1 Banach Center Publications

3 Saal L.

1 Cardoso I.

1 Faraut J.

1 2012

1 2010

1 2007

A Wiener type theorem for (U(p,q),Hₙ)

Explicit fundamental solutions of some second order differential operators on Heisenberg groups

The Wigner semi-circle law and the Heisenberg group