Related papers: Notes on the Chernoff estimate

Recently, Kayumov \cite{K} obtained a sharp estimate for the $n$-th truncated area functional for normalized functions in the Bloch space for $n\le 5$ and then, together with Wirths \cite{KW1}, extended the result for $n=6$. We prove that…

Let $A$ be an unbounded operator on a Banach space $X$. It is sometimes useful to improve the operator $A$ by extending it to an operator $B$ on a larger Banach space $Y$ with smaller spectrum. It would be preferable to do this with some…

We generalize the Strichartz estimates for Schr\"odinger operators on compact manifolds of Burq, G\'erard and Tzvetkov [10] by allowing critically singular potentials $V$. Specifically, we show that their $1/p$--loss $L^p_tL^q_x(I\times…

We present a general method of solving the Cauchy problem for a linear parabolic partial differential equation of evolution type with variable coefficients and demonstrate it on the equation with derivatives of orders two, one and zero. The…

This paper explores the concept of approximate Birkhoff-James orthogonality in the context of operators on semi-Hilbert spaces. These spaces are generated by positive semi-definite sesquilinear forms. We delve into the fundamental…

In this paper, we consider estimation of the conditional mode of an outcome variable given regressors. To this end, we propose and analyze a computationally scalable estimator derived from a linear quantile regression model and develop…

Our main aim is to investigate the approximation properties for the summation integral type operators in a statistical sense. In this regard, we prove the statistical convergence theorem using well known Korovkin theorem and the degree of…

Inspired by topological Wiener-Wintner theorems we study the mean ergodicity of amenable semigroups of Markov operators on $C(K)$ and show the connection to the convergence of strong and weak ergodic nets. The results are then used to…

his paper deals with approximating properties of the newly defined $q$-generalization of the Sz\'{a}sz operators in the case $q>1$. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem…

We employ combinatorial techniques to present an explicit formula for the coefficients in front of Chern classes involving in the Hattori-Stong integrability conditions. We also give an evenness condition for the signature of stably…

There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…

We consider the Cauchy problem for Schr\"odinger type operators. Under a suitable decay assumption on the imaginary part of the first order coefficients we prove well-posedness of the Cauchy problem in Gelfand-Shilov classes. We also…

In this paper, we provide a unifying theory concerning the convergence properties of the so-called max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. The approximation of functions…

Within the superfield formalism, we calculate the two-point functions and the effective potential for the mass-deformed ${\cal N}=3$ Chern-Simons-matter theory and discuss the related renormalization group issues.

We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in…

In this paper we prove analogues of Korovkin's theorem in the context of weakly nonlinear and monotone operators acting on Banach lattices of functions of several variables. Our results concern the convergence almost everywhere, the…

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…

In this paper, we establish sharp bounds for a family of Kantorovich-type neural network operators within the general frameworks of Sobolev-Orlicz and Orlicz spaces. We establish both strong (in terms of the Luxemburg norm) and weak (in…

This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…

We show well-posedness for an evolution problem associated with the Dirichlet-to-Robin operator for certain Robin boundary data. Moreover, it turns out that the semigroup generated by the Dirichlet-to-Robin operator is closely related to a…