This article derives the distribution of random matrix X associated with the transformation Y = X*X, such that Y has a Riesz distribution for real normed division algebras. Two versions of this distributions are proposed and some of their properties are studied.

We derive sharp Adams inequalities with exact growth condition for the Riesz potential and more general Riesz-like potentials on Rn. also obtain Moser-Trudinger fractional Laplacian, homogeneous elliptic differential operators constant coefficients.

In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.

We consider a gas of N particles subject to two-body interaction and confined by an external potential in the mean field or high temperature regime, that is when inverse ?>0 satisfies ?N???0 as N?+?. show under general conditions on potential, local fluctuations are described Poisson point process large limit. present applications Coulomb Riesz gases Rn for any n?1, well edge behavior ?-ensembl...

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...

1. Compact operators on Banach spaces 2. Appendix: total boundedness and Arzela-Ascoli [Fredholm 1900/1903] treated compact operators as limiting cases of finite-rank operators. [1] [Riesz 1917] defined and made direct use of the compactness condition, more apt for Banach spaces. See [Riesz-Nagy 1952] for extensive discussion in the Hilbert-space situation, and many references to original paper...