On Zero Sets in the Dirichlet Space

Zero sets in pointfree topology and strongly $z$-ideals

In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...

The Dirichlet Space on the bi-disc

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acknowledge the importance of e-commerce to their countries and to survival of their businesses and in creating and encouraging an atmosphere for the wide adoption and success of e-commerce in the long term. the investment for implementing e-commerce in the public sector is one of the areas which is focused in government‘s action plan for cross-disciplinary it development and e-readiness in go...

Bilinear Forms on the Dirichlet Space

Hankel operators on the Hardy space of the disk, H (D) , can be studied as linear operators from H (D) to its dual space, as conjugate linear operators from H (D) to itself, or, in the viewpoint we will take here, as bilinear functionals on H (D) × H (D) . In that formulation, given a holomorphic symbol function b we consider the bilinear Hankel form, defined initially for f, g in P (D) , the s...

The classical Dirichlet space

D |f ′|2 dx dy. In particular, we will cover the basic structure of these functions their boundary values and their zeros along with two important operators that act on this space of functions the forward and backward shifts. This survey is by no means complete. For example, we will not cover the Toeplitz or Hankel operators on these functions, nor will we cover the important topic of interpola...