### (Fba)- and (FBB)-spaces.

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Estudiamos algunas cuestiones estructurales acerca del espacio localmente convexo H , que está formado por funciones analíticas en el disco unidad abierto. Construimos una descomposición atómica de este espacio, usando un retículo de puntos del disco unidad que es más denso que el usual. También demostramos que H no es nuclear.

We study Toeplitz operators ${T}_{a}$ with radial symbols in weighted Bergman spaces ${A}_{\mu}^{p}$, 1 < p < ∞, on the disc. Using a decomposition of ${A}_{\mu}^{p}$ into finite-dimensional subspaces the operator ${T}_{a}$ can be considered as a coefficient multiplier. This leads to new results on boundedness of ${T}_{a}$ and also shows a connection with Hardy space multipliers. Using another method we also prove a necessary and sufficient condition for the boundedness of ${T}_{a}$ for a satisfying an assumption on the positivity of certain indefinite...

It is well known that one can often construct a star-product by expanding the product of two Toeplitz operators asymptotically into a series of other Toeplitz operators multiplied by increasing powers of the Planck constant h. This is the Berezin-Toeplitz quantization. We show that one can obtain in a similar way in fact any star-product which is equivalent to the Berezin-Toeplitz star-product, by using instead of Toeplitz operators other suitable mappings from compactly supported smooth functions...

We study the linearized water-wave problem in a bounded domain (a finite pond of water) of ${\mathbb{R}}^{3}$, having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point $\mathcal{O}$ of the water surface, where a submerged body touches the surface (see Fig. 1). The radiation...

When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset $G\subset {\u2102}^{N}$ which play an important role in the projective description problem. A number of relevant examples are provided, and a “new projective description problem” is posed. The proof of our main result can also serve to characterize...

We consider Bergman projections and some new generalizations of them on weighted ${L}^{\infty}\left(\right)$-spaces. A new reproducing formula is obtained. We show the boundedness of these projections for a large family of weights v which tend to 0 at the boundary with a polynomial speed. These weights may even be nonradial. For logarithmically decreasing weights bounded projections do not exist. In this case we instead consider the projective description problem for holomorphic inductive limits.

We study the linearized water-wave problem in a bounded domain ( a finite pond of water) of ${\mathbb{R}}^{3}$, having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point $\mathcal{O}$ of the water surface, where a submerged body touches the surface (see Fig. 1). The...

In this paper we introduce and investigate classes of Fréchet and (DF)-spaces which constitute a very general frame in which the problem of topologies of Grothendieck and some related dual questions have a positive answer. Many examples of spaces in theses classes are provided, in particular spaces of sequences and functions. New counterexamples to the problems of Grothendieck are given.

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