In recent papers, the Right and the Strong* topologies have been introduced and studied on general Banach spaces. We characterize different types of continuity for multilinear operators (joint, uniform, etc.) with respect to the above topologies. We also study the relations between them. Finally, in the last section, we relate the joint Strong*-to-norm continuity of a multilinear operator T defined on C*-algebras (respectively, JB*-triples) to C*-summability (respectively, JB*-triple-summability)....

For the hypoelliptic differential operators $P={\partial }_x^2+{\left(x^k{\partial }_y-x^l{\partial }_t\right)}^2$ introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of $k$ and $l$ left open in the analysis, the operators $P$ also fail to be analytic hypoelliptic (except for $(k,l)=(0,1)$), in accordance with Treves’ conjecture. The proof is constructive, suitable for generalization, and relies on evaluating a family of eigenvalues of a non-self-adjoint operator.

Ortega-Cerdà-Seip demonstrated that there are bounded multiplicative Hankel forms which do not arise from bounded symbols. On the other hand, when such a form is in the Hilbert-Schmidt class ₂, Helson showed that it has a bounded symbol. The present work investigates forms belonging to the Schatten classes between these two cases. It is shown that for every $p>{(1-log\pi /log4)}^{-1}$ there exist multiplicative Hankel forms in the Schatten class ${}_p$ which lack bounded symbols. The lower bound on p is in a certain sense optimal...

On montre que le faisceau $ℱ$ des sursolutions locales dans $W_{\mathrm{loc}}^2$ d’un certain opérateur elliptique $L$ est maximal pour un principe du minimum adapté aux espaces de Sobolev. La continuité de la réduite variationnelle des éléments continus permet alors d’étudier des représentants s.c.i.

Several properties of balayage of measures in harmonic spaces are studied. In particular, characterisations of thinness of subsets are given. For the heat equation the following result is obtained: suppose that $E={\mathbf{R}}^{m+1}$ is given the presheaf of solutions of$$\sum _{i=1}^m\frac{\partial u}{\partial x_i}=\frac{\partial u}{\partial x_{m+1}}$$and $B$ is a subset of ${\mathbf{R}}^m\times [-\infty ,0]$ satisfying$$\left\{\right(\alpha x,{\alpha }^{2}t):(x,t)\in B,x\in {\mathbf{R}}^m,t\in \mathbf{R}\}\subset B$$for $\alpha \>0$ arbitrarily small. Then $B$ is thin at 0 if and only if $B$ is polar. Similar result for the Laplace equation. At last the reduced of measures is defined and several approximation theorems on reducing and balayage...

We give a complete characterization of the positive trigonometric polynomials $Q(\theta ,\varphi )$ on the bi-circle, which can be factored as $Q(\theta ,\varphi )=|p(e^{i\theta },e^{i\varphi }){|}^2$ where $p(z,w)$ is a polynomial nonzero for $\left|z\right|=1$ and $\left|w\right|\le 1$. The conditions are in terms of recurrence coefficients associated with the polynomials in lexicographical and reverse lexicographical ordering orthogonal with respect to the weight $\frac{1}{4{\pi }^{2}Q(\theta ,\varphi )}$ on the bi-circle. We use this result to describe how specific factorizations of weights on the bi-circle can be translated into identities relating...

This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups with Wentzell boundary conditions in the characteristic case. Our results may be stated as follows: We can construct Feller semigroups corresponding to a diffusion phenomenon including absorption, reflection, viscosity, diffusion along the boundary and jump at each point of the boundary.

A method to study the embedded point spectrum of self-adjoint operators is described. The method combines the Mourre theory and the Limiting Absorption Principle with the Feshbach Projection Method. A more complete description of this method is contained in a joint paper with V. Jak$\check{\mathrm{s}}$ić, where it is applied to a study of embedded point spectrum of Pauli-Fierz Hamiltonians.