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.

and Applied Analysis 3 Wj and W̃j of Vj and Ṽj , respectively, satisfying Vj 1 Vj ̇Wj , Wj ⊥ Ṽj and Ṽj 1 Ṽj ̇W̃j , W̃j ⊥ Vj . The corresponding biorthogonal wavelets are given by ψj ∑ n∈Z −1 ã j 1−nφj 1 2 · −n , ψ̃j ∑ n∈Z −1 a j 1−nφ̃j 1 2 · −n . 1.4 A generalization of the biorthogonal wavelets of Cohen-Daubechies-Feuveau 1 was introduced that was based on exponential B-splines 12 . By generalizing...

Let E be a Banach space that does not contain any copy of l and A be a non commutative C∗-algebra. We prove that every absolutely summing operator from A into E∗ is compact, thus answering a question of Pe lczynski. As application, we show that if G is a compact metrizable abelian group and Λ is a Riesz subset of its dual then every countably additiveA∗-valued measure with bounded variation and...

A Green's function for a generalized two-dimensional (2D) fluid in an unbounded domain (the so-called α turbulence system) is discussed. The generalized 2D fluid is characterized by a relationship between an advected quantity q and the stream function ψ : namely, q=-(-Δ){α/2}ψ . Here, α is a real number and q is referred to as the vorticity. In this study, the Green's function refers to the str...

A stable intermediate dimeric G-rich form as a precursor of tetrameric G-quadruplex structures has been detected via MALDI-TOF spectrometry. Molecular dynamics simulation offered detailed insights at the atomic level, assigning reverse Watson-Crick G-G base pairing (not Hoogsteen) in the G-rich dimer. In support of this, cisplatin formed a stable adduct by binding to the dimeric G-rich structur...

This is the first in a series of two papers in which we construct a convolution product for associated homogeneous distributions (AHDs) with support in R. In this paper, we show that if f and g are AHDs with degrees of homogeneity a−1 and b−1, the convolution fa∗gb exists as an AHD, provided the resulting degree of homogeneity a + b − 1 is not a natural number. Under this restriction, it is fou...