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Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…
The maximum principle is one of the most important tools in the analysis of geometric partial differential equations. Traditionally, the maximum principle is applied to a scalar function defined on a manifold, but in recent years more…
Value distribution and uniqueness problems of difference operator of an entire function have been investigated in this article. This research shows that a finite ordered entire function $ f $ when sharing a set $ \mathcal{S}=\{\alpha(z),…
We apply Rossi's half-plane version of Borel's Theorem to study the zero distribution of linear combinations of $\mathcal{A}$-entire functions (Theorem 1.2). This provides a unified way to study linear $q$-difference, difference and…
This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set. Moreover, we will give the existence of unique range sets for meromorphic functions that are zero sets of polynomials that do not…
This theorem is based on holomorphy of studied functions and the fact that near a singularity point the real part of some rational function can take an arbitrary preassigned value.
Partition of unities appear in many places in analysis. Typically they are generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire…
We show that if a complex entire function $f$ and its derivative $f'$ share their simple zeroes and their simple $a$-points for some nonzero constant $a$, then $f\equiv f'$. We also discuss how far these conditions can be relaxed or…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We present a fixed point theorem for a class of (potentially) non-monotonic functions over specially structured complete lattices. The theorem has as a special case the Knaster-Tarski fixed point theorem when restricted to the case of…
We consider the zeros distributions on the derivatives of difference polynomials of meromorphic functions, and present some results which can be seen as the discrete analogues of Hayman conjecture \cite{hayman1}, also partly answer the…
We prove the existence and pointwise bounds of the Green functions for stationary Stokes systems with measurable coefficients in two dimensional domains. We also establish pointwise bounds of the derivatives of the Green functions under a…
We calculate the exact zeros of the partition function for a continuum system where the probability distribution for the order parameter is given by two asymmetric Gaussian peaks. When the positions of the two peaks coincide, the two…
This paper systematically investigates the analytic properties of the ratio $f(s)/f(1-s) = X(s)$ based on the Davenport-Heilbronn functional equation $f(s) = X(s)f(1-s)$. We propose a novel method to analyze the distribution of non-trivial…
The Riemann problem is studied in the case when the unknown function has nonisolated singularities, concentrated on the real axis. The problem is used for the factorization of functions, holomorphic outside of the unit circle and the real…
We study the set of chords of a real-valued continuous function on [0,1] with f(0)=f(1)=0. We describe which chords may appear as isolated points and provide examples illustrating our characterization. Maximal Hopf sets are introduced and…
We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the…
A new integral identity for functions with continuous second partial derivatives is derived. It is shown that the value of any function f(r,t) at position r and time t is completely determined by its previous values at all other locations…
We study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions arise in the application of implicit s-stage, order p…