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1
Content available remote

Hankel convolution on distribution spaces with exponential growth

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J. Betancor J., Rodríguez-Mesa L.
Studia Mathematica
|
1996
|
tom 121
|
nr 1
35-52
EN
We study the Hankel transformation and Hankel convolution on spaces of distributions with exponential growth.
2
Content available remote

Solving dual integral equations on Lebesgue spaces

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Ciaurri Ó., Guadalupe J. J., Pérez M., Varona J. L.
Studia Mathematica
|
2000
|
tom 142
|
nr 3
253-267
EN
We study dual integral equations associated with Hankel transforms, that is, dual integral equations of Titchmarsh's type. We reformulate these equations giving a better description in terms of continuous operators on $L^p$ spaces, and we solve them in these spaces. The solution is given both as an operator described in terms of integrals and as a series $∑_{n=0}^{∞} c_n J_{μ+2n+1}$ which converges in the $L^p$-norm and almost everywhere, where $J_ν$ denotes the Bessel function of order ν. Finally, we study the uniqueness of the solution.
3
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A convolution operation for a distributional Hankel transformation

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J. Betancor J., González B. J.
Studia Mathematica
|
1995-1996
|
tom 117
|
nr 1
57-72
EN
We investigate the Hankel transformation and the Hankel convolution on new spaces of generalized functions.
4
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Characteristic polynomials of sample covariance matrices: The non-square case

100%
Kösters H.
Open Mathematics
|
2010
|
tom 8
|
nr 4
763-779
EN
We consider the sample covariance matrices of large data matrices which have i.i.d. complex matrix entries and which are non-square in the sense that the difference between the number of rows and the number of columns tends to infinity. We show that the second-order correlation function of the characteristic polynomial of the sample covariance matrix is asymptotically given by the sine kernel in the bulk of the spectrum and by the Airy kernel at the edge of the spectrum. Similar results are given for real sample covariance matrices.
5
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Representations of Jordan algebras and special functions

100%
Travaglini G.
Colloquium Mathematicum
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1991
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tom 62
|
nr 2
257-266
EN
This paper is concerned with the action of a special formally real Jordan algebra U on an Euclidean space E, with the decomposition of E under this action and with an application of this decomposition to the study of Bessel functions on the self-adjoint homogeneous cone associated to U.
6
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Polydisc slicing in $ℂ^n$

100%
Oleszkiewicz K., Pełczyński A.
Studia Mathematica
|
2000
|
tom 142
|
nr 3
281-294
EN
Let D be the unit disc in the complex plane ℂ. Then for every complex linear subspace H in $ℂ^n$ of codimension 1, $vol_{2n-2}(D^{n-1}) ≤ vol_{2n-2}(H ∩ D^{n}) ≤ 2vol_{2n-2}(D^{n-1})$. The lower bound is attained if and only if H is orthogonal to the versor $e_{j}$ of the jth coordinate axis for some j = 1,...,n; the upper bound is attained if and only if H is orthogonal to a vector $e_{j} + σe_{k}$ for some 1 ≤ j < k ≤ n and some σ ∈ ℂ with |σ| = 1. We identify $ℂ^n$ with $ℝ^{2n}$; by $vol_{k}(·)$ we denote the usual k-dimensional volume in $ℝ^{2n}$. The result is a complex counterpart of Ball's [B1] result for cube slicing.
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