Related papers: Nigel Kalton and complex interpolation of compact …
The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.
Although the study of functional calculus has already established necessary and sufficient conditions for operators to be fractionalized, this paper aims to use our well-conceived notion of integer powers of operators to construct…
In this paper we revisit the classical problem of polynomial interpolation, with a slight twist; namely, polynomial evaluations are available up to a group action of the unit circle on the complex plane. It turns out that this new setting…
Suppose that (A_0,A_1) and (B_0,B_1) are Banach couples, and that T is a linear operator which maps A_0 compactly into B_0 and A_1 boundedly (or even compactly) into B_1. Does this imply that T maps [A_0,A_1]_s to [B_0,B_1]_s compactly for…
We solve an interpolation problem in $A^p_\alpha$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative at the $k^{\textrm{th}}$ point is up to a constant as large as possible for functions…
In this paper we analyze iterations of the obstacle problem for two different operators. We solve iteratively the obstacle problem from above or below for two different differential operators with obstacles given by the previous functions…
We formulate the issue of minimality of self-adjoint operators on a Hilbert space as a semi-definite problem, linking the work by Overton in [1] to the characterization of minimal hermitian matrices. This motivates us to investigate the…
It is demonstrated that any almost-tilting module over a gentle algebra is indeed partial-tilting, meaning it can be completed as a tilting module. Furthermore, such a module has at most $2n$ possible complements, thereby confirming a…
For the inclusion problem involving two maximal monotone operators, under the metric subregularity of the composite operator, we derive the linear convergence of the generalized proximal point algorithm and several splitting algorithms,…
The present review presents the authors previous results on the topic from the title in a new light. Most of the previous results were obtained using the techniques of antilinear Hilbert-Schmidt mappings of one Hilbert pace into another,…
We propose a new primal-dual splitting method for solving composite inclusions involving Lipschitzian, and parallel-sum-type monotone operators. Our approach extends the framework in \cite{Siopt4} to a more general class of monotone…
We use reproducing kernel methods to study various rigidity problems. The methods and setting allow us to also consider the non-positive case.
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…
The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of first order logic, which are amenable for…
This note is devoted to the study of Hyt\"{o}nen's extrapolation theorem of compactness on weighted Lebesgue spaces. Two criteria of compactness of linear operators in the two-weight setting are obtained. As applications, we obtain…
A time-variant analogue of an interpolation problem equivalent to the relaxed commutant lifting problem is introduced and studied. In a somewhat less general form the problem already appears in the analysis of the set of all solutions to…
By using some techniques of the divided difference operators, we establish an 4n-point interpolation formula. Certain polynomials, such as Jackson's _8\phi_7 terminating summation formula, are special cases of this formula. Based on…
We consider a wide class of semi linear Hamiltonian partial differential equa- tions and their approximation by time splitting methods. We assume that the nonlinearity is polynomial, and that the numerical tra jectory remains at least uni-…
In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the…
This expository thesis contains a study of four interpolation theorems, the requisite background material, and a few applications. The materials introduced in the first three sections of Chapter 1 are used to motivate and prove the…