Related papers: On the index of meromorphic operator-valued functi…
We introduce a generalized index for certain meromorphic, unbounded, operator-valued functions. The class of functions is chosen such that energy parameter dependent Dirichlet-to-Neumann maps associated to uniformly elliptic partial…
We study several natural multiplicity questions that arise in the context of the Birman-Schwinger principle applied to non-self-adjoint operators. In particular, we re-prove (and extend) a recent result by Latushkin and Sukhtyaev by…
The general spectral boundary value problem framework is utilized to restate boundary value problems of Poincare, Hilbert, and Riemann for harmonic and analytic functions in abstract operator-theoretic terms.
A multiple operator integral (MOI) is an indispensable tool in several branches of noncommutative analysis. However, there are substantial technical issues with the existing literature on the "separation of variables" approach to defining…
This is the first of two papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
Reference [1] established an index theory for a class of linear selfadjoint operator equations covering both second order linear Hamiltonian systems and first order linear Hamiltonian systems as special cases. In this paper based upon this…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
We study algebraic properties of Toeplitz operators on Bergman spaces of polyanalytic functions on the unit disk. We obtain results on finite-rank commutators and semi-commutators of Toeplitz operators with harmonic symbols. We also raise…
We consider operator-valued Herglotz functions and their applications to self-adjoint perturbations of self-adjoint operators and self-adjoint extensions of densely defined closed symmetric operators. Our applications include model…
We develop the Titchmarsh-Weyl theory for vector-valued discrete Schr\"odinger operators and show that the Weyl $m$ functions associated with these operators map complex upper half plane to the Siegel upper half space. We also discuss about…
In this paper, recent abstract multiplier theorems for $0$-sectorial and $0$-strip type operators by Kriegler and Weis (2018) are refined and generalized to arbitrary sectorial and strip-type operators. To this end, holomorphic…
The notion of quasi boundary triples and their Weyl functions from extension theory of symmetric operators is extended to the general framework of adjoint pairs of operators under minimal conditions on the boundary maps. With the help of…
The operator-valued multiplier theorems in weighted abstract Besov spaces are studied. These results permit us to show embedding theorems in weighted Besov-Lions type spaces. The most regular class of interpolation space is found such that…
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…
We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
We introduce and study weighted spaces of functions with mixed norm on the upper half-plane, defined in terms of Fourier transform. We give a characterization of analytic functions within these spaces, and in particular, we provide an…
A certain class of matrix-valued Borel matrix functions is introduced and it is shown that all functions of that class naturally operate on any operator T in a finite type I von Neumann algebra M in a way such that uniformly bounded…