Related papers: Friedrichs extensions for a class of singular disc…
Time-fractional parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are discretized in time using continuous collocation methods. For such discretizations, we give sufficient conditions for existence and uniqueness…
We introduce a novel technique for proving global strong discrete maximum principles for finite element discretizations of linear and semilinear elliptic equations for cases when the common, matrix-based sufficient conditions are not…
The paper provides an explicit description of the structure of the domain of the Friedrichs extension of a second order semibounded elliptic wedge operator, initially defined on smooth functions or sections with compact support away from…
In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.
The concept of extended Hamiltonian systems allows the geometrical interpretation of several integrable and superintegrable systems with polynomial first integrals of degree depending on a rational parameter. Until now, the procedure of…
We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms…
In our article [15] description in terms of abstract boundary conditions of all $m$-accretive extensions and their resolvents of a closed densely defined sectorial operator $S$ have been obtained. In particular, if $\{\mathcal{H},\Gamma\}$…
A family $\mathcal{T}^{(\nu)}$, $\nu\in\mathbb{R}$, of semiinfinite positive Jacobi matrices is introduced with matrix entries taken from the Hahn-Exton $q$-difference equation. The corresponding matrix operators defined on the linear hull…
In this work, firstly in the Hilbert space of vector-functions L^2 (H,(-\infty,a)\bup(b,+\infty)),a<b all selfadjoint extensions of the minimal operator generated by linear singular symmetric differential expression l(\cdot)=i d/dt+A with a…
In this paper we prove strong unique continuation principle and unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open domain. Our proofs are based on the…
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, {we give conditions under which these…
Recent breakthrough methods \cite{gggz,joux,bgjt} on computing discrete logarithms in small characteristic finite fields share an interesting feature in common with the earlier medium prime function field sieve method \cite{jl}. To solve…
In this paper, we mainly establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for a class of fully nonlinear second-order elliptic equations related to the eigenvalues of the Hessian, with…
Using closed positive extensions of the quadratic form in the potential term we provide alternative solutions to the eigenstate equation for the free quantum field Hamiltonian in the Schr\"o\-din\-ger representation. We show that admissible…
The A-model for finite rank singular perturbations of class $\mathfrak{H}_{-m-2}\smallsetminus\mathfrak{H}_{-m-1}$, $m\in\mathbb{N}$, is considered from the perspective of boundary relations. Assuming further that the Hilbert spaces…
We consider Hamiltonian systems in first-order multisymplectic field theories. We review the properties of Hamiltonian systems in the so-called restricted multimomentum bundle, including the variational principle which leads to the…
In this work we prove uniqueness result for an implicit discrete system defined on connected graphs. Our discrete system is motivated from a certain class of spatial segregation of reaction-diffusion equations.
Hamilton's principle does not formally apply to systems whose boundary conditions lie outside configuration space, but extensions are possible using certain "natural" boundary conditions that allow action extremization. With the single…
Solving functional equations given in \cite{nagy} for extensions of a group $A$ by a weighted Steiner loop $S$ we obtain concrete description for all loops with interesting weak associativity properties if the Steiner loop $S$ induces only…
The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic…