Related papers: A note on analytic continuation of characteristic …
In this paper we collect several examples of convergence of functions of random processes to generalized functionals of those processes. We remark that the limit is always finitely absolutely continuous with respect to Wiener measure. We…
It is known that the Cauchy's argument principle, applied to an holomorphic function $f$, requires that $f$ has no zeros on the curve of integration. In this short note, we give a generalization of such a principle which covers the case…
This paper presents a necessary and sufficient condition for a real-valued function defined on an open and convex subset of a Banach space to be quasi-concave, and a sufficient condition for such a function to be strictly quasi-concave.…
Nevanlinna showed that Cauchy transforms of probability measures parametrize all functions from the upper half plane into itself satisfying a certain asymptotic condition at infinity. We show that the correspondence fails in general for the…
It is shown (Theorem A and its corollary) that if g is any nonconstant nonunivalent analytic function on a half-plane H and if D is either a half-plane or a smoothly bounded Jordan domain, then there is a function f on D for which f'(D)…
If $f$ is a Henstock--Kurzweil integrable function on the real line, the Alexiewicz norm of $f$ is $\|f\|=\sup_I|\int_I f|$ where the supremum is taken over all intervals $I\subset\R$. Define the translation $\tau_x$ by $\tau_xf(y)=f(y-x)$.…
We introduce a new type of test for complete spatial randomness that applies to mapped point patterns in a rectangle or a cube of any dimension. This is the first test of its kind to be based on characteristic functions and utilizes a…
We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two…
We discuss a general result of holomorphic extension of a real analytic function $f$ defined on the boundary $\partial D$ of a real analytic strictly convex subset $D\subset\subset \C^n$. We show that this follows from the hypothesis of…
Arakeljan's Theorem provides conditions on a relatively closed subset $F$ of a domain $G\subset\mathbb{C}$, such that any continuous function $f:F\rightarrow\mathbb{C}$ that is analytic in $F^\circ$, can be approximated by analytic…
We give some necessary and some sufficient conditions for the complete monotonicity on the negative half-line of a Mittag-Leffler function of Le Roy type. It is conjectured that the underlying positive random variable, when it exists, must…
In this paper, we discuss the representability almost everywhere (a.e.) in the plane of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite…
Let U be the closed unit disc in C and let p be a point on the unit circle. Let f be a continuous function on U which extends holomorphically from each circle contained in U and centered at the origin, and from each circle contained in U…
We study the Cauchy problem for the quasi-geostrophic equations with the critical dissipation in the two dimensional half space under the homogeneous Dirichlet boundary condition. We show the global existence, the uniqueness and the…
An extension $K/k$ of analytic (i.e. real valued complete) fields is called small if it is topologically-algebraically generated by finitely many elements. We prove that this property is inherited by subextensions and hence topological…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
In this paper we give a generalization and improvement of the Pavlovi\'{c} result on the characterization of continuously differentiable functions in the Bloch space on the unit ball in $\mathbb{R}^m$. Then we derive a Holland--Walsh type…
In classical function theory, a function is holomorphic if and only if it is complex analytic. For higher dimensional spaces it is natural to work in the context of Clifford algebras. The structures of these algebras depend on the parity of…
We study continuity and regularity of convex extensions of functions from a compact set $C$ to its convex hull $K$. We show that if $C$ contains the relative boundary of $K$, and $f$ is a continuous convex function on $C$, then $f$ extends…
Analytic approximations of functions of Cayley-Dickson variables are investigated. The case of functions of complexified Cayley-Dickson variables is also encompassed. Moreover, extensions of functions of Cayley-Dickson variables are…