Related papers: Bounded Multilinear Functionals and Multicontinuou…

Kostyrko and Salat showed that if a linear space of bounded functions has an element that is discontinuous almost everywhere, then a typical element in the space is discontinuous almost everywhere. We give a topological analogue of this…

We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally…

Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…

Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…

We study a concept of inner function suited to Dirichlet-type spaces. We characterize Dirichlet-inner functions as those for which both the space and multiplier norms are equal to 1.

Gleason's theorem asserts the equivalence of von Neumann's density operator formalism of quantum mechanics and frame functions, which are functions on the pure states that sum to 1 on any orthonormal basis of Hilbert space of dimension at…

We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We…

A quasi-product on the normed space is defined. In addition, the notions of the eigenvectors of a linear operator can be extended for the nonlinear operator. Based on the quasi-product and the generalized eigenvectors, the spectral theorems…

A two-dimensional threshold function of k-valued logic can be viewed as coloring of the points of a k x k square lattice into two colors such that there exists a straight line separating points of different colors. For the number of such…

In this article we give an approach to define continuous functional calculus for bounded quaternionic normal operators defined on a right quaternionic Hilbert space.

We discuss five simple functions on finite multisets of metric spaces. The first four are all metrics iff the underlying space is bounded and are complete metrics iff it is also complete. Two of them, and the fifth function, all generalise…

We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…

Let $\Gamma$ be a Polish space and let $K$ be a separable and pointwise compact set of real-valued functions on $\Gamma$. It is shown that if each function in $K$ has only countably many discontinuities then $C(K)$ may be equipped with a…

We consider finite sums of counting functions on the free group $F_n$ and the free monoid $M_n$ for $n \geq 2$. Two such sums are considered equivalent if they differ by a bounded function. We find the complete set of linear relations…

In this paper, the relationship between notions of observability for continuous-time nonlinear system related to distinguishability, observability rank condition and K-function has been investigated. It is proved that an autonomous…

In this paper, we study functions of bounded variation on a complete and connected metric space with finite one-dimensional Hausdorff measure. The definition of BV functions on a compact interval based on pointwise variation is extended to…

In this paper, first we present a new useful way of formulating probabilistic normed spaces. Then by using this formulation and probabilistic normed space version of the Baire category theorem, we prove four important results of functional…

A Boolean $k$-monotone function defined over a finite poset domain ${\cal D}$ alternates between the values $0$ and $1$ at most $k$ times on any ascending chain in ${\cal D}$. Therefore, $k$-monotone functions are natural generalizations of…

Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…

Let M be a simply-connected complete Kahler manifold whose sectional curvature is bounded between two negative numbers. In this paper we prove the existence of non-constant bounded holomorphic functions on M if the complex dimension of M is…