Related papers: On evolutionary equations related to skew-symmetri…
We consider the recursion operators with nonlocal terms of special form for evolution systems in (1+1) dimensions, and extend them to well-defined operators on the space of nonlocal symmetries associated with the so-called universal Abelian…
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…
There is constructed and considered the extension of classical Diriclet operator corresponding to uniformly log-concave measure in the space of symmetric differential forms. Sufficient conditions for its essential self-adjointness in…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild solution is derived and a general error…
We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…
A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…
Initial-boundary value problems for complex sine-Gordon and sine-Gordon equations in a semi--strip are treated. The evolution of the Weyl function and a uniqueness result are obtained for complex sine-Gordon equation. The evolution of the…
In this paper, we propose new algorithms for finding a common point of the solution set of a pseudomonotone equilibrium problem and the set of fixed points of a symmetric generalized hybrid mapping in a real Hilbert space. The convergence…
The resolution of a very large class of linear and non-linear, stationary and evolutive partial differential problems in the half-space (or similar) under the slip boundary condition is reduced here to that of the corresponding results for…
A recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their…
Equivariant localization expresses global invariants in terms of local invariants, and many of them appearing in equivariant index theory, (holomorphic) Morse theory, geometric quantization and supersymmetric localization can be…
A semiclassical approximation for an evolving density operator, driven by a "closed" hamiltonian operator and "open" markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the…
Shift Harnack and integration by part formula are establish for semilinear spde with delay and a class of stochastic semilinear evolution equation which cover the hyperdissipative Naiver-Stokes/Burges equation. For the case of stochastic…
We consider infinite-dimensional parabolic rough evolution equations. Using regularizing properties of analytic semigroups we prove global-in-time existence of solutions and investigate random dynamical systems for such equations.
Results on stability of tautological sheaves on Hilbert schemes of points are extended to higher dimensions and transferred to abelian surfaces and to the restriction of tautological sheaves to generalised Kummer varieties. This provides a…
We revise Krein's extension theory of positive symmetric operators. Our approach using factorization through an auxiliary Hilbert space has several advantages: it can be applied to non-densely defined transformations and it works in both…
A symmetric characteristic singular integral equation with two fixed singularities at the endpoints in the class of functions bounded at the ends is analyzed. It reduces to a vector Hilbert problem for a half-disc and then to a vector…
We study the general properties of spectral curves associated to doubly-periodic solutions of Korteweg-deVries, sine-Gordon, Non-linear Schr\"odinger and 1D Toda equations, and construct examples of arbitrary genus.
We prove an abstract criterion that a surjective convolution operator in spaces of analytic functions on convex subsets of the complex plane has a continuous linear right inverse. Considered convex sets have a countable neighborhood basis…