Related papers: Analyticity and propagation of plurisubharmonic si…
The addition of certain nonrenormalizable terms to the usual action density of a free scalar field leads to nonrenormalizable theories whose exact euclidian and minkowskian Green's functions are less singular than those of the free theory.…
Let $X$ be a real analytic orbifold. Then each stratum of $X$ is a subanalytic subset of $X$. We show that $X$ has a unique subanalytic triangulation compatible with the strata of $X$. We also show that every ${\rm C}^r$-orbifold, $1\leq…
In this article, we present univalence criteria for polyharmonic and polyanalytic functions. Our approach yields new a criterion for a polyharmonic functions to be fully $\alpha$--accessible. Several examples are presented to illustrate the…
Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.
In this paper, we employ the theory of normal families in several complex variables to obtain some uniqueness theorems for entire functions. These results extend the related works of Li and Yi [11], and Lu et al. [18] to the setting of…
We develop and use some key concepts of potential theory, such as balayage and duality between measures and their potentials, to study the distribution of masses of subharmonic functions while restrictions to their growth near the boundary…
In this work, we generalize previous results about the Fractionary Schr\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate…
We consider finite relational signatures $\tau \subseteq \sigma$, a sequence of finite base $\tau$-structures $(\mathcal{B}_n : n \in \mathbb{N})$ the cardinalities of which tend to infinity and such that, for some number $\Delta$, the…
We consider the dynamics of expanding semigroups generated by finitely many rational maps on the Riemann sphere. We show that for an analytic family of such semigroups, the Bowen parameter function is real-analytic and plurisubharmonic.…
We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest…
We review and give elementary proofs of Liouville type properties of harmonic and subharmonic functions in the plane endowed with a complete Riemannian metric, and prove a gap theorem for the possible growth of harmonic functions when this…
In this paper has been proved the pluripolarity of graphs of algebroid functions
We prove a Pucci-Serrin conjecture on critical dimensions under a uniform bound on the energy. The method is based on the analysis of the Green's function of polyharmonic operators with "almost" Hardy potential.
Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.
Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.
We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers.
We show that Green functions of second-order differential operators with singular or unbounded coefficients can have an anomalous behaviour in comparison to the well-known properties of Green functions of operators with bounded…
The concept of proximate order is widely used in the theories of entire, meromorphic, subharmonic and plurisubharmonic functions. We give a general interpretation of this concept as a proximate growth function relative to a model growth…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
There are ten chapters in this dissertation, which focuses on nine contents: growth estimates for a class of subharmonic functions in the half plane; growth estimates for a class of subharmonic functions in the half space; a generalization…