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We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with strongly regular sequences, we establish generalizations of…
A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with the help of a family of weight functions is considered in this paper. For…
We study the relative growth of finitely generated subgroups in finitely generated groups, and the corresponding distortion function of the embeddings. We explore which functions are equivalent to the relative growth functions and…
Recently, Chatterjee has introduced a new coefficient of correlation which has several natural properties. In particular, the coefficient attains its maximal value if and only if one variable is a measurable function of the other variable.…
A class of subharmonic functions represented by the modified kernels are proved to have the growth estimates $u(z)= o(y^{1-\alpha}|z|^{m+\alpha})$ at infinity in the upper half plane ${\bf C}_{+}$, which generalizes the growth properties of…
We introduce a join construction as a way of completing the description of the relative conormal space of an analytic function on a complex analytic space that has a non-vanishing derivative at the origin. Then we show how to obtain a…
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
In [2] we characterized in terms of a quadratic growth condition various metric regularity properties of the subdifferential of a lower semicontinuous convex function acting in a Hilbert space. Motivated by some recent results in [16] where…
The "qualitative" extension theorem of Demailly guarantees existence of holomorphic extensions of holomorphic sections on some subvariety under certain positive-curvature assumption, but that comes without any estimate of the extensions,…
A Daniell-Stone type characterization theorem for Aumann integrals of set-valued measurable functions will be proven. It is assumed that the values of these functions are closed convex upper sets, a structure that has been used in some…
A class of subharmonic functions represented by the modified kernels are proved to have the growth estimates u(x) =o(x_{n}^{1-alpha}|x|^{m+alpha})at infinity in the upper half space of Rn, which generalizes the growth properties of analytic…
In the present paper, we obtain a more general conditions for univalence of analytic functions in the open unit disk U. Also, we obtain a refinement to a quasiconformal extension criterion of the main result.
This paper mainly studies the quadratic growth and the strong metric subregularity of the subdifferential of a function that can be represented as the sum of a function twice differentiable in the extended sense and a subdifferentially…
We give a general strategy to construct superoscillating/growing functions using an orthogonal polynomial expansion of a bandlimited function. The degree of superoscillation/growth is controlled by an anomalous expectation value of a…
The goal of this paper is to unify the theory of weights beyond the setting of weighted Lebesgue spaces in the general setting of quasi-Banach function spaces. We prove new characterizations for the boundedness of singular integrals, pose…
We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…
In previous work, we showed that an anomaly in the one point function of marginal operators is related by the Wess-Zumino condition to the Euler density anomaly on a two dimensional defect or boundary. Here we analyze in detail the two…
Several growth models have been proposed in the literature for scale-free complex networks, with a range of fitness-based attachment models gaining prominence recently. However, the processes by which such fitness-based attachment behaviour…
We apply recent knowledge and techniques of the new generalized upper and lower Legendre conjugates to the theory of weight functions in the sense of Braun-Meise-Taylor and study in detail the effects on the corresponding associated weight…
We provide new necessary and sufficient conditons for ensuring strong quasiconvexity in the nonsmooth case and, as a consequence, we provide a proof for the differentiable case. Furthermore, we improve the quadratic growth property for…