Zero sets of analytic function spaces on the unit disk
Kaptanoğlu, Hakkı Turgay
Item Usage Stats
MetadataShow full item record
We survey some known results on the zero sets of two families of analytic function spaces and another single space de ned on the unit disk in the complex plane. We investigate mostly the basic properties of the zero sets of these spaces that are comparable to those of the Hardy spaces and to each other. The spaces we consider are standard weighted Bergman spaces, the Dirichlet space, and certain Dirichlet-type spaces that are very close to both Hardy spaces and the Bergman spaces. The completely known zero sets of Hardy spaces are easy to describe, characterized by the Blaschke condition and the same for all the spaces in the family. The zero sets of the other spaces considered have started to be investigated relatively recently and are far from a complete description. Yet it is possible to nd conditions similar to the Blaschke condition for the zero sets of Bergman spaces and Dirichlet-type spaces. For the zero sets of the true Dirichlet space, the known results are sporadic and do not form a general theory yet.
Showing items related by title, author, creator and subject.
Ertuğrul, Zehra (Bilkent University, 1994)This work is a study of the relation between the vanishing of Ext functor and the existence of regular bases in the cartesian product and tensor product of some special Kothe spaces. We give some new results concerning ...
Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product Oktem, F. S.; Ozaktas, H. M. (Optical Society of America, 2010-07-30)Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique ...
Ozaktas, H. M.; Oktem, F. S. (Optical Society of America., 2013)We show how to explicitly determine the space-frequency window (phase-space window) for optical systems consisting of an arbitrary sequence of lenses and apertures separated by arbitrary lengths of free space. If the ...