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The optimal sufficient conditions for the $L^p$-to-$L^q$ compactness of commutators of singular integral operators of both Calder\'on-Zygmund and of rough type are shown in the different exponent ranges $``q>p"$, $``q=p"$ and $``q<p"$ to…
We develop the compactness theory of multilinear singular integrals on product spaces using a modern point of view. The first main result is a compact $T1$ theorem for multilinear Calder\'{o}n--Zygmund operators on product spaces. More…
We define a zeta function woth respect to the twisted Grover matrix of a mixed digraph, and present an exponential expression and a determinant expression of this zeta function. As an application, we give a trace formula with respect to the…
We investigate some analytic properties of traces of Dirichlet forms with respect to measures satisfying Hardy-type inequality. Among other results we prove convergence of spectra, ordered eigenvalues, eigenfunctions as well as convergence…
In this text we consider discrete Laplace operators defined on lattices based on finitely-ramified self-similar sets, and their continuous analogous defined on the self-similar sets themselves. We are interested in the spectral properties…
We introduce a generalized trace functional TR in the spirit of Kontsevich and Vishik's canonical trace for classical SG-pseudodifferential operators on R^n and suitable manifolds, using a finite-part integral regularization technique. This…
In this paper, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and the quasiperiodic boundary conditions. Using these…
The principal aim in this paper is to develop an effective and unified approach to the computation of traces of resolvents (and resolvent differences), Fredholm determinants, $\zeta$-functions, and $\zeta$-function regularized determinants…
We introduce a general method of extending (pseudo-)metrics from X to FX, where F is a normal functor on the category of metrizable compacta. For many concrete instances of F, our method specializes to the known constructions.
In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For {\it arbitrary} self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized…
We obtain several essential self-adjointness conditions for a Schroedinger type operator D*D+V acting in sections of a vector bundle over a manifold M. Here V is a locally square-integrable bundle map. Our conditions are expressed in terms…
We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic $\alpha$-Farey maps. We provide a family of observables which are Riemann integrable, locally constant and of bounded variation, and for which the…
We give a complete classification and present new exotic phenomena of the meromorphic structure of $\zeta$-functions associated to general self-adjoint extensions of Laplace-type operators over conic manifolds. We show that the meromorphic…
The Laplace operator admits infinite self-adjoint extensions when considered on a segment of the real line. They have different domains of essential self-adjointness characterized by a suitable set of boundary conditions on the wave…
We study self-adjoint extensions of operators which are the product of the multiplication operator by an analytic function and the analytic continuation in a strip. We compute the deficiency indices of the product operator for a wide class…
A Master equation has been previously obtained which allows the analytic integration of a fairly large family of functions provided that they possess simple properties. Here, the properties of this Master equation are explored, by extending…
This work develops an analytic framework for the study of the $\zeta$-function associated with general sequences of complex numbers. We show that a contour integral representation, commonly used when studying spectral $\zeta$-functions…
We obtain inequalities for the Riesz means for the discrete spectrum of a class of self-adjoint compact integral operators. Such bounds imply some inequalities for the counting function of the Dirichlet boundary problem for the Laplace…
Spectral boundary conditions for Laplace-type operators, of interest in string and brane theory, are partly Dirichlet, partly Neumann-type conditions, partitioned by a pseudodifferential projection. We give sufficient conditions for…
We compute the Dixmier trace of pseudo-Toeplitz operators on the Fock space. As an application we find a formula for the Dixmier trace of the product of commutators of Toeplitz operators on the Hardy and weighted Bergman spaces on the unit…