Related papers: Coercivity estimates for integro-differential oper…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
The separate tasks of denoising, least squares expectation, and manifold learning can often be posed in a common setting of finding the conditional expectations arising from a product of two random variables. This paper focuses on this more…
We consider a class of constant-coefficient partial differential operators on a finite-dimensional real vector space which exhibit a natural dilation invariance. Typically, these operators are anisotropic, allowing for different degrees in…
The aim of this work is to present the regularity condition (also known in the literature as structure condition) an integro-differential operator may satisfy in order for the domination principle to hold for (sub-,super-) solutions of…
In this paper, we introduce a new semi-norm of operators on a semi-Hilbertian space, which generalizes the A-numerical radius and A-operator semi-norm. We study the basic properties of this semi-norm, including upper and lower bounds for…
Sharp resolvent bounds for non-selfadjoint semiclassical elliptic quadratic differential operators are established, in the interior of the range of the associated quadratic symbol.
In this paper, we propose a new concept of derivative with respect to an arbitrary kernel-function. Several properties related to this new operator, like inversion rules, integration by parts, etc. are studied. In particular, we introduce…
We find an explicit integral formula for the eigenfunctions of a fourth order differential operator against the kernel involving two Bessel functions. Our formula establishes the relation between K-types in two different realizations of the…
We introduce a novel conditional density estimation model termed the conditional density operator (CDO). It naturally captures multivariate, multimodal output densities and shows performance that is competitive with recent neural…
In this manuscript we define the right fractional derivative and its corresponding right fractional integral with exponential kernel. Then, we provide the integration by parts formula and we use $Q-$operator to confirm our results. The…
In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error bounds for reduced-order modeling; extension of these…
In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…
Recent decades have provided a host of examples and applications motivating the study of nonlocal differential operators. We discuss a class of such operators acting on bounded domains, focusing on those with integrable kernels having…
Using the method of similar operators we study an even order differential operator with periodic, semiperiodic, and Dirichlet boundary conditions. We obtain asymptotic formulas for eigenvalues of this operator and estimates for its spectral…
In this paper, we employ probabilistic techniques to derive sharp, explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator $$ \Delta^{\alpha/2}_v + v \cdot \nabla_x, \quad \alpha \in (0, 2),\ (x,v)\in {\mathbb…
We study nonparametric estimation for the partially conditional average treatment effect, defined as the treatment effect function over an interested subset of confounders. We propose a hybrid kernel weighting estimator where the weights…
We prove a Weitzenb\"ock identity for general pairs of constant coefficient homogeneous first order partial differential operators, and deduce from it sufficient algebraic conditions for coerciveness and Morrey estimates under the natural…
The six-vertex model with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is obtained. The kernel of the corrtesponding integral operator depends on Laguerre…
We consider skew-symmetric operators $A_{0}$ on a Hilbert space $H$ and characterise all (nonlinear) m-accretive restrictions of $A:=-A_{0}^{\ast}$ in terms of the "deficiency spaces" $\ker(1\pm A)$. The results are illustrated by several…
The conversion of resolvent conditions into semigroup estimates is crucial in the stability analysis of hyperbolic partial differential equations. For two families of multiple Toeplitz operators, we relate the power bound with a resolvent…