Related papers: Separable Quadratic Stochastic Operators
We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent…
In this work we study some general classes of pseudodifferential operators whose symbols are defined in terms of phase space estimates.
We consider periodic matrix-valued Jacobi operators. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the Lyapunov function, which is analytic on an associated Riemann surface. On…
In this paper we give the answers to two open questions on complex symmetric composition operators. By doing this, we give a complete description of complex symmetric composition operators whose symbols are linear fractional.
The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary…
We find shift operators for the Dotsenko-Fateev equation, which is a differential equation of order 3, and for the three Fuchsian differential equations of order 4, 5 and 6, respectively, which are connected with the Dotsenko-Fateev…
This paper provides a method to study the non-negativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and non-negative, we can study the complex powers…
We develop Cresson's nondifferentiable calculus of variations on the space of H\"{o}lder functions. Several quantum variational problems are considered: with and without constraints, with one and more than one independent variable, of first…
Sharp resolvent bounds for non-selfadjoint semiclassical elliptic quadratic differential operators are established, in the interior of the range of the associated quadratic symbol.
Real and complex norms of a linear operator acting on a normed complexified space are considered. Bounds on the ratio of these norms are given. The real and complex norms are shown to coincide for four classes of operators: 1) real linear…
For a system of linear partial differential equations (LPDEs) we introduce an operator equation for auxiliary operators. These operators are used to construct a kernel of an integral transformation leading the LPDE to the separation of…
Contents 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of…
Recent work by several authors has revealed the existence of many unexpected classes of normal weighted composition operators. On the other hand, it is known that every normal operator is a complex symmetric operator. We therefore undertake…
Many applications require stochastic processes specified on two- or higher-dimensional domains; spatial or spatial-temporal modelling, for example. In these applications it is attractive, for conceptual simplicity and computational…
We consider the Krall-Sheffer class of admissible, partial differential operators in the plane. We concentrate on algebraic structures, such as the role of commuting operators and symmetries. For the polynomial eigenfunctions, we give…
Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and…
We suggest to investigate certain non-standard (pseudo-)differential operators in order to construct and to study multi-parameter processes. Our approach will include "classical" multi-parameter Markov processes but will go eventually far…
The use of operator-splitting methods to solve differential equations is widespread, but the methods are generally only defined for a given number of operators, most commonly two. Most operator-splitting methods are not generalizable to…
Parameter--elliptic pseudodifferential operators given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev…
We study the pseudospectrum of a class of non-selfadjoint differential operators. Our work consists in a detailed study of the microlocal properties, which rule the spectral stability or instability phenomena appearing under small…