Cyclicity in Reproducing Kernel Hilbert Spaces of analytic functions Articles uri icon

publication date

  • December 2014

start page

  • 665

end page

  • 680

issue

  • 4

volume

  • 14

International Standard Serial Number (ISSN)

  • 1617-9447

Electronic International Standard Serial Number (EISSN)

  • 2195-3724

abstract

  • We introduce a large family of reproducing kernel Hilbert spaces H⊂Hol(D), which include the classical Dirichlet-type spaces Dalfa, by requiring normalized monomials to form a Riesz basis for H. Then, after precisely evaluating the nth optimal norm and the n-th approximant of f(z)=1−z, we completely characterize the cyclicity of functions in Hol(D¯¯¯¯) with respect to the forward shift.

keywords

  • cyclicity; optimal approximation