Related papers: Gelfand-Yaglom formula for functional determinants…
We consider the fractional Laplacian on a domain and investigate the asymptotic behavior of its eigenvalues. Extending methods from semi-classical analysis we are able to prove a two-term formula for the sum of eigenvalues with the leading…
This paper presents a new formulation of the fractional Laplacian operator $(-\Delta)^s$ in $n$-dimensional space ($n \ge 1$). The proposed formulation expresses $(-\Delta)^s$ as a composition of the classical Laplace differential operator…
We study the properties of linear and non-linear determining functionals for dissipative dynamical systems generated by PDEs. The main attention is payed to the lower bounds for the number of such functionals. In contradiction to the common…
In this paper, we investigate dimension-free estimates for maximal operators of convolutions with discrete normalized Gaussians (related to the Theta function) in the context of maximal, jump and $r$-variational inequalities on…
We introduce more general concepts of Riemann-Liouville fractional integral and derivative on time scales, of a function with respect to another function. Sufficient conditions for existence and uniqueness of solution to an initial value…
In this paper we analyze the spectral zeta function associated with a Laplace operator acting on scalar functions on an N-dimensional Euclidean space in the presence of a spherically symmetric background potential. The obtained analytic…
Monotone operators, especially in the form of subdifferential operators, are of basic importance in optimization. It is well known since Minty, Rockafellar, and Bertsekas-Eckstein that in Hilbert space, monotone operators can be understood…
For a closed Riemannian manifold $(M,g)$ of dimension $n$, let $\lambda_{1}(g)$ be the first positive eigenvalue of the Laplace--Beltrami operator $\Delta_{g}$ and $\mbox{Vol}(M,g)$ the volume of $(M, g)$. Considering the scale-invariant…
In this paper, we derive certain formulas giving the Laplace transforms of two generalized fractional integral operators introduced recently in [Fract. Calc. Appl. Anal. 20 (2) (2017), 422--446]. The main results provide generalizations to…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
In this work we propose a generalization of the Hadamard product between two matrices to a tensor-valued, multi-linear product between k matrices for any $k \ge 1$. A multi-linear dual operator to the generalized Hadamard product is…
We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order…
We generate Gaussian radial function based higher order compact RBF-FD formulas for some differential operators. Analytical expressions for weights associated to first and second derivative formulas (up to order 10) and 2D-Laplacian…
Generalized spectra of differential operators can be related to spectra of preconditioned discretized operators. Obtaining (estimates of) the eigenvalues of the preconditioned discretized operators may lead to better estimating of the…
This paper explores the global properties of time-independent systems of operators in the framework of Gelfand-Shilov spaces. Our main results provide both necessary and sufficient conditions for global solvability and global…
In this paper our purpose is to find upper bound estimate for the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for functions defined by convolution belonging to the class $\mathcal{N}_{\sigma}^{\mu,\delta}(\lambda,t)$ by using…
Integral representations play a prominent role in the analysis of entire functions. The representations of generalized Mittag-Leffler type functions and their asymptotics have been (and still are) investigated by plenty of authors in…
We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterisation of such operators is performed in the Laplace domain it is…
We study the point spectrum of a second order difference operator with complex potential on the half-line via Fredholm determinants of the corresponding Birman-Schwinger operator pencils, the Evans and the Jost functions. An application is…
We explicitly give factorization formulas for higher depth determinants, which are defined via derivatives of the spectral zeta function at non-positive integer points, of Laplacians on the n-sphere in terms of the multiple gamma functions.