Related papers: A question by Alexei Aleksandrov and logarithmic d…
We prove logarithmic Sobolev inequalities for semi-direct product operators (see definition in Section 1). We apply our main results to examples of operators and provide some applications to ultracontractive bounds of semigroups. Hardy's…
An $A_{\infty}$-weight on a Lipschitz curve $\Lambda$ in the plane can be extended analytically to the graph Lipschitz domain $\Omega$ above it. This problem was studied by C. Kenig [Ken80], who introduced the class $AE$ of well-behaved…
We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space $H^2$ on the unit disc. This answers a question posed by Shapiro and Sundberg in 1990. We also establish…
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…
In this note, we prove Cheng-Yau type local gradient estimate for harmonic functions on Alexandrov spaces with Ricci curvature bounded below. We adopt a refined version of Moser's iteration which is based on Zhang-Zhu's Bochner type…
We show that for any positive integer $d$, there are families of switched linear systems---in fixed dimension and defined by two matrices only---that are stable under arbitrary switching but do not admit (i) a polynomial Lyapunov function…
We determine the Lusztig restrictions on the space of class functions with a unipotent support on a finite reductive group. In particular we give a simple expression for the Lusztig restrictions of the generalized Green functions and we…
A concept of boundedness of L-index in joint variables (see in Bordulyak M.T. The space of entire in $\mathbb{C}^n$ functions of bounded L-index, Mat. Stud., 4 (1995), 53--58. (in Ukrainian)) is generalised for analytic in a bidisc…
We prove a Liouville type classification theorem in half-spaces for infinite boundary value problems related to fully nonlinear, uniformly elliptic operators. We then apply the result in order to obtain gradient boundary blow up rates for…
We set up a left ring of fractions over a certain ring of boundary problems for linear ordinary differential equations. The fraction ring acts naturally on a new module of generalized functions. The latter includes an isomorphic copy of the…
We give upper bounds on the eigenvalues of the differential form Laplacian on a compact Riemannian manifold. The proof uses Alexandrov spaces with curvature bounded below. We also construct differential form Laplacians on Alexandrov spaces.…
In this paper we use a method based on the Grunsky coefficients to find upper bounds of the modulus of the initial coefficients, difference of the moduli of two consecutive initial coefficients, of the modulus of the initial logarithmic…
The $S$-functional calculus for slice hyperholomorphic functions generalizes the Riesz-Dunford-functional calculus for holomorphic functions to quaternionic linear operators and to $n$-tuples of noncommuting operators. For an unbounded…
Let $\mathcal{S}^*(\varphi)$ be the class of all analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$, normalized by $f(0)=f'(0)-1=0$ that satisfy the subordination relation $zf'(z)/f(z)\prec\varphi(z)$, where…
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and…
We continue the work begun by Mickler-Moll investigating the properties of the polynomial eigenfunctions of the Nazarov-Sklyanin quantum Lax operator. By considering products of these eigenfunctions, we produce a novel generalization of a…
Working in the p-adic analog of the complex numbers, we'll define a line integral on a small arc of a circle. This allows new versions of the Residue Theorem, the Cauchy-Goursat Theorem on discs with and without holes, Cauchy's Integral…
A conjecture of I. Krasikov is proved. Several discrete analogues of classical polynomial inequalities are derived, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-P\'olya class.
Let $\mathcal{U(\alpha, \lambda)}$, $0<\alpha <1$, $0 < \lambda <1$ be the class of functions $f(z)=z+a_{2}z^{2}+a_{3}z^{3}+\cdots$ satisfying $$\left|\left(\frac{z}{f(z)}\right)^{1+\alpha}f'(z)-1\right|<\lambda$$ in the unit disc ${\mathbb…
We make systematic developments on Lawson-Osserman constructions relating to the Dirichlet problem (over unit disks) for minimal surfaces of high codimension in their 1977 Acta paper. In particular, we show the existence of boundary…