Related papers: Reflectionless measures for Calder\'on-Zygmund Ope…
We analyze reflection positive representations in terms of positive Hankel operators. This is motivated by the fact that positive Hankel operators are described in terms of their Carleson measures, whereas the compatibility condition…
We extend the method for constructing symmetry operators of higher order for two-dimensional quantum Hamiltonians by Kalnins, Kress and Miller (2010). This expansion method expresses the integral in a finite power series in terms of lower…
Using the sine-Gordon model as the prime example an alternative approach to integrable boundary conditions for a theory restricted to a half-line is proposed. The main idea is to explore the consequences of taking into account the…
In a series of papers, M.Talagrand, the second author and others investigated at length the properties and structure of pointwise compact sets of measurable functions. A number of problems, interesting in themselves and important for the…
Motivated by a question of L. Robert, asking whether $\rm L(T(A)) = Lsc_{C}(T(A))$ for any separable C*-algebra A, we introduce and initiate the study of \emph{tracially reflexive C*-algebras}. We first prove that commutative C*-algebras…
The main goal of this work is to introduce an analogous in the non-archimedean context of the Gelfand spaces of certain Banach commutative algebras with unit. In order to do that, we study the spectrum of this algebras and we show that,…
We construct a class of singular integral operators associated with homogeneous Calder\'{o}n-Zygmund standard kernels on $d$-dimensional, $d <1$, Sierpinski gaskets $E_d$. These operators are bounded in $L^2(\mu_d)$ and their principal…
We establish a new $T1$ theorem for the compactness of bi-parameter Calder\'on-Zygmund singular integral operators. Namely, we show that if a bi-parameter CZO $T$ satisfies the product weak compactness property, the mixed weak…
In the first section we provide a solution to the M. G. Krein problem about an inner description of the space $L_2(\Sigma,H).$ In the second section we introduce the multiplicity function for an operator measure. Making use of the…
I consider general reflection coefficients for arbitrary one-dimensional whole line differential or difference operators of order $2$. These reflection coefficients are semicontinuous functions of the operator: their absolute value can only…
We develop a wide general theory of bilinear bi-parameter singular integrals $T$. First, we prove a dyadic representation theorem starting from $T1$ assumptions and apply it to show many estimates, including $L^p \times L^q \to L^r$…
We prove a multilinear local $T(b)$ theorem that differs from previously considered multilinear local $T(b)$ theorems in using exclusively general testing functions $b$ as opposed to a mix of general testing functions and indicator…
One defines a non-homogeneous space $(X, \mu)$ as a metric space equipped with a non-doubling measure $\mu$ so that the volume of the ball with center $x$, radius $r$ has an upper bound of the form $r^n$ for some $n> 0$. The aim of this…
In the absence of a half-bound state, a compactly supported potential of a Schr\"odinger operator on the line is determined up to a translation by the zeros and poles of the meropmorphically continued left (or right) reflection coefficient.…
We introduce and study a class of analytic difference operators admitting reflectionless eigenfunctions. Our construction of the class is patterned after the Inverse Scattering Transform for the reflectionless self-adjoint Schr\"odinger and…
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…
We provide an alternative proof of a (local) T1 theorem for dual exponents in the non-homogeneous setting of upper doubling measures. This previously known theorem provides necessary and sufficient conditions for the L^p-boundedness of…
This paper investigates the properties of trajectories in harmonic oscillator systems equipped with a point, absolutely continuous, or singular measure. As demonstrated in [30], infinite-dimensional linear flows of countable oscillator…
The finite Hilbert transform $T$, when acting in the classical Zygmund space $\logl$ (over $(-1,1)$), was intensively studied in \cite{curbera-okada-ricker-log}. In this note an integral representation of $T$ is established via the…
A proof of the Riemann hypothesis using the reflection principle is presented.