Common zero sets of equivalent singular inner functions

Singular sets of Sobolev functions

Zero Sets for Spaces of Analytic Functions

We show that under mild conditions, a Gaussian analytic function F that a.s. does not belong to a given weighted Bergman space or Bargmann–Fock space has the property that a.s. no non-zero function in that space vanishes where F does. This establishes a conjecture of Shapiro (1979) on Bergman spaces and allows us to resolve a question of Zhu (1993) on Bargmann–Fock spaces. We also give a simila...

Singular values of convex functions of matrices

‎Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $‎sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $‎sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$  are nonzero matrices and each $X_{i}$ is‎ ‎positive semidefinite‎. ‎It is shown that if $f$ is a nonnegative increasing ‎convex function on $left[ 0,infty right) $ satisfying $fleft( 0right)‎ ‎=0 $‎, ‎then  $$‎2s_{j}left( fleft( fra...

Zero sets of holomorphic functions in the bidisc

In this work we characterize the zero sets of holomorphic functions f in the bidisc such that log jf j Lp D p Moreover we give a su cient condition on a analytic variety to be de ned by a function in A D Introduction In this paper we study some geometrical conditions on analytic varieties in the bidisc D fz C jz j jz j g to be de ned by an holomorphic func tion with some restriction on its grow...

Common acoustical pole and zero modeling of room transfer functions

Abstruct-A new model for a room transfer function (RTF) by using common acoustical poles that correspond to resonance properties of a room is proposed. These poles are estimated as the common values of many RTF’s corresponding to different source and receiver positions. Since there is one-to-one correspondence between poles and AR coefficients, these poles are calculated as common AR coefficien...