Abstract Let μ \mu be a positive Borel measure on the interval [ 0 , 1 ) \left[0,1) . The Hankel matrix H = ( n <m:m...

We compare the rate of decay singular numbers a given composition operator acting on various Hilbert spaces analytic functions unit disk D. show that for Hardy and Bergman spaces, our results are sharp. also give lower upper estimates with symbol “cusp map” lens maps, weighted Dirichlet spaces.

In this paper, the Fredholm properties of some Toeplitz operators on Dirichlet spaces be discussed, and the essential spectra of Toeplitz operators with symbols in C 1 or H ∞ 1 + C 1 be computed.

In order to treat certain "non-symmetric" potential theories, It6 I-4] and Bliedtner [1] have generalized Beurling and Deny's theory of Dirichlet spaces by replacing the inner product in the Dirichlet space with a bilinear form defined on a real, regular functional space. This bilinear form, called a Dirichlet form, is supposed to be continuous and coercive, and furthermore to satisfy a "contra...