Related papers: On linearisation and uniqueness of preduals

The main focus of this paper is to study multi-valued linear monotone operators in the contexts of locally convex spaces via the use of their Fitzpatrick and Penot functions. Notions such as maximal monotonicity, uniqueness,…

In this paper, first we study surjective isometries (not necessarily linear) between completely regular subspaces $A$ and $B$ of $C_0(X,E)$ and $C_0(Y,F)$ where $X$ and $Y$ are locally compact Hausdorff spaces and $E$ and $F$ are normed…

Let $A$ be a square matrix and let $\Omega$ be an open set in the plane containing the spectrum of $A$. We consider the problem of maximizing the operator norm $\|f(A)\|$ amongst all holomorphic functions $f$ from $\Omega$ into the closed…

We consider functional equations driven by linear fractional transformations, which are special cases of de Rham's functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a…

We define the strong shortcut property for rough geodesic metric spaces, generalizing the notion of strongly shortcut graphs. We show that the strong shortcut property is a rough similarity invariant. We give several new characterizations…

Let $L$ be a Riesz space with a strong unit $e>0$.$\mathfrak{\ }$We show that a unital linear functional $H:L\rightarrow \mathbb{R}$ satisfies $% H\left( u\right) \neq 0$ for any strong unit $u\in L$ if and only if $H$ acts like a Riesz…

We characterize a holomorphic positive definite function $f$ defined on a horizontal strip of the complex plane as the Fourier-Laplace transform of a unique exponentially finite measure on $\mathbb{R}$. The classical theorems of Bochner on…

In this note the following is proved. Separable L-embedded spaces - that is separable Banach spaces which are complemented in their biduals such that the norm between the two complementary subspaces is additive - have property (X) which, by…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…

The thesis concentrates on two problems in discrete geometry, whose solutions are obtained by analytic, probabilistic and combinatoric tools. The first chapter deals with the strong polarization problem. This states that for any sequence…

The number of distinct symbols appearing in digit expansions generated by full-branch affine countable iterated function systems is studied whose branch weights are regularly varying. The Hausdorff dimensions of the exceptional sets in…

We introduce the notion of a strong L-space, a closed, oriented rational homology 3-sphere whose Heegaard Floer homology can be determined at the chain level. We prove that the fundamental group of a strong L-space is not left-orderable.…

Let $F$ be an ordered topological vector space (over $\mathbb{R}$) whose positive cone $F_+$ is weakly closed, and let $E \subseteq F$ be a subspace. We prove that the set of positive continuous linear functionals on $E$ that can be…

We study Caratheodory-Herglotz functions whose values are continuous operators from a locally convex topological space which admits the factorization property into its conjugate dual space. We show how this case can be reduced to the case…

Imposing a strong condition on the linear order of shellable complexes, we introduce strong shellability. Basic properties, including the existence of dimension-decreasing strong shelling orders, are developed with respect to nonpure…

We consider normalized univalent functions with prescribed second Taylor coefficient $a_2$. For convex functions $f$ we study the Hardy spaces to which $f$ and $f'$ belong, refining in particular on a theorem of Eenigenburg and Keogh, and…

We obtain $C^2$ a priori estimates for solutions of the nonlinear second-order elliptic equation related to the geometric problem of finding a strictly locally convex hypersurface with prescribed curvature and boundary in a space form.…

An old question of A.V. Arhangel'skii asks if the Menger property of a Tychonoff space $X$ is preserved by homeomorphisms of its function space $C_p(X)$. We provide affirmative answer in the case of linear homeomorphisms. To this end, we…

Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…

We present an idea of unifying small scale (topology, proximity spaces, uniform spaces) and large scale (coarse spaces, large scale spaces). It relies on an analog of multilinear forms from Linear Algebra. Each form has a large scale…