Physical Sciences and Mathematics Commons^™

Approximation Of Invariant Subspaces, Faruk Yilmaz

Doctoral Dissertations

For a real number α [alpha] the Dirichlet-type spaces 𝔇_α [script D sub alpha] are the family of Hilbert spaces consisting of all analytic functions f(z) = ∑_n=0^∞[sum over n equals zero to infinity] ˆf(n) [f hat of n] zⁿ [z to the n] defined on the open unit disc 𝔻 [unit disc] such that

∑_n=0^∞ (n+1)^α | ˆf(n) |²

[sum over n equals 0 to infinity] [(n+1) to α] [ | f hat of n | to 2]

is finite.

For α < 0, the spaces 𝔇_α are known as weighted Bergman spaces. When …