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Several recent papers investigated unbounded and statistical versions of order convergence and topology convergence in locally solid Riesz space. In this papers, we study the statistical unbounded order and topology convergence in Riesz…
We prove in this article that every Borelian measure, for example, the distribution of a random variable, in separable Banach space has a support which is compact embedded Banach subspace; and prove that if the norm of the random variable…
In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a…
The paper is concerned with the problem whether a nonseparable Banach space must contain an uncountable set of vectors such that the distances between every two distinct vectors of the set are the same. Such sets are called equilateral. We…
We lift upper and lower estimates from linear functionals to $n$-homogeneous polynomials and using this result show that $l_\infty$ is finitely represented in the space of $n$-homogeneous polynomials, $n\ge2$, for any infinite dimensional…
We study a class of chainable continua which contains, among others, all inverse limit spaces generated by a single interval bonding map which is piecewise monotone and locally eventually onto. Such spaces are realized as attractors of…
We study the inhomogeneous linear system which arises in the higher order asymptotic expansion of the wave functions of multi-component Bose-Einstein condensates, across the regular part of the interface, in the case of segregation.
We give a new scale of completeness conditions for exponential systems in two types of functional spaces on subsets of the complex plane. The first is the Banach spaces of functions that are continuous on a compact and simultaneously…
We investigate for which compactifications $\gamma\omega$ of the discrete space of natural numbers $\omega$, the natural copy of the Banach space $c_0$ is complemented in $C(\gamma\omega)$. We show, in particular, that the separability of…
We consider the algebra of invariants of $d$-tuples of $n\times n$ matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic $p$ different from two. It is well-known that this…
Coherence, the superposition of orthogonal quantum states, is indispensable in various quantum processes. Inspired by the polynomial invariant for classifying and quantifying entanglement, we first define polynomial coherence measure and…
Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from the geometry of homogeneous space. Furthermore, our work…
There exists a real hereditarily indecomposable Banach space $X$ such that the quotient space $L(X)/S(X)$ by strictly singular operators is isomorphic to the complex field (resp. to the quaternionic division algebra). Up to isomorphism, the…
By using quasi-Banach techniques as key ingredient we prove Poincar\'e- and Sobolev- type inequalities for $m$-subharmonic functions with finite $(p,m)$-energy. A consequence of the Sobolev type inequality is a partial confirmation of B\l…
We study an infinite class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. This generalizes a sequence of sparse polynomials which arises in a natural way as graph theoretic…
Mixture quality plays a crucial role in the physical properties of multi-component immiscible polymer mixtures including nanocomposites and polymer blends. Such complex mixtures are often characterized by hierarchical internal structures,…
For a large class of separable Banach spaces, we prove the real analytic Dolbeault Isomorphism Theorem for open subsets.
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…
This paper deals with extensions or twisted sums of Banach spaces that come induced by complex interpolation and the relation between the type and cotype of the spaces in the interpolation scale and the nontriviality and singularity of the…
Small ball inequalities have been extensively studied in the setting of Gaussian processes and associated Banach or Hilbert spaces. In this paper, we focus on studying small ball probabilities for sums or differences of independent,…