Related papers: Multi-dimensional Besicovitch almost periodic type…
In this paper, we discuss the relationships between stability and almost periodicity for solutions of stochastic differential equations. Our essential idea is to get stability of solutions or systems by some inherited properties of Lyapunov…
We study a new class of functions that arise naturally in quaternionic analysis, we call them "quasi regular functions". Like the well-known quaternionic regular functions, these functions provide representations of the quaternionic…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
We introduce Schur multiple zeta functions which interpolate both the multiple zeta and multiple zeta-star functions of the Euler-Zagier type combinatorially. We first study their basic properties including a region of absolute convergence…
We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that…
We explore the relationship in metric spaces between different properties related to the Besicovitch covering theorem, and also consider weak versions of doubling, in connection to the non-uniqueness of centers and radii in arbitrary metric…
We consider one dimensional chains of interacting particles subjected to one dimensional almost-periodic media. We formulate and prove two KAM type theorems corresponding to both short-range and long-range interactions respectively. Both…
In the last years it has been shown that Lotka-Volterra mappings constitute a valuable tool from both the theoretical and the applied points of view, with developments in very diverse fields such as Physics, Population Dynamics, Chemistry…
We construct the quasi-classical approximation of the form factors in finite volume using the separation of variables. The latter is closely related to the Baxter equation.
Using C. Fefferman's embedding of a charge space in a measure space allows us to apply standard interpolation theorems to prove norm inequalities for Besicovitch almost periodic functions. This yields an analogue of Paley's Inequality for…
The piecewise-concave function may be used to approximate a wide range of other functions to arbitrary precision over a bounded set. In this short paper, this property is proven for three function classes: (a) the multivariate twice…
Based on recent developments in the theory of fractional Sobolev spaces, an interesting new class of nonlocal variational problems has emerged in the literature. These problems, which are the focus of this work, involve integral functionals…
We introduce a definition of intrinsically quasi-symmetric sections in metric spaces and we prove the Ahlfors-David regularity for this class of sections. We follow a recent result by Le Donne and the author where we generalize the notion…
We study multiplication as well as Nemytskij operators in anisotropic vector-valued Besov spaces $B^{s, \omega}_p$, Bessel potential spaces $H^{s, \omega}_p$, and Sobolev-Slobodeckij spaces $W^{s, \omega}_p$. Concerning multiplication we…
The purpose of this work is to investigate root finding problems defined on (quasi-)metric spaces, and ranging in Euclidean spaces. The motivation for this line of inquiry stems from recent models in biology and phylogenetics, where…
We prove a new vectorial functional inequality of Poincar\'{e}-Beckner type. The inequality may be interpreted as an entropy-entropy production one for a gradient flow in the metric space of Radon measures. The proof uses subtle analysis of…
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
This is a survey about certain "almost homomorphisms" and "almost linear" functionals (called quasi-morphisms and quasi-states) in symplectic topology and their applications to Hamiltonian dynamics, functional-theoretic properties of…
In the present paper, we introduce the notion of nearly holomorphic Drinfeld modular forms and study an analogue of Maass-Shimura operators in this context. Furthermore, for a given nearly holomorphic Drinfeld modular form, we show that its…