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Comparative approximation in two topologies

H. Shapiro — 1979

Banach Center Publications

A counterexample in harmonic analysis

H. Shapiro — 1979

Banach Center Publications

Zeros of random functions in Bergman spaces

Joel H. Shapiro — 1979

Annales de l'institut Fourier

Suppose $μ$ is a finite positive rotation invariant Borel measure on the open unit disc $Δ$ , and that the unit circle lies in the closed support of $μ$ . For $0 < p < \infty$ the $A_{μ}^{p}$ is the collection of functions in $L^{p} (μ)$ holomorphic on $Δ$ . We show that whenever a Gaussian power series $f (z) = Σ ζ_{n} a_{n} z^{n}$ almost surely lies in $A_{μ}^{p}$ but not in $⋃_{q > p} A_{μ}^{p}$ , then almost surely: a) the zero set $Z (f)$ of $f$ is not contained in any $A_{μ}^{q}$ zero set ( $q > p$ , and b) $Z (f + 1) \cup Z (f - 1)$ is not contained in any $A_{μ}^{q}$ zero set.

Interpolation in Hilbert spaces of analytic functions

H. Shapiro; A. Shields — 1963

Studia Mathematica

Some properties of N-supercyclic operators

P. S. Bourdon; N. S. Feldman; J. H. Shapiro — 2004

Studia Mathematica

Let T be a continuous linear operator on a Hausdorff topological vector space 𝓧 over the field ℂ. We show that if T is N-supercyclic, i.e., if 𝓧 has an N-dimensional subspace whose orbit under T is dense in 𝓧, then T* has at most N eigenvalues (counting geometric multiplicity). We then show that N-supercyclicity cannot occur nontrivially in the finite-dimensional setting: the orbit of an N-dimensional subspace cannot be dense in an (N+1)-dimensional space. Finally, we show that a subnormal operator...

Totally bounded uniformities

R. A. Alò; H. L. Shapiro — 1974

Commentationes Mathematicae

The article contains no abstract

Cyclic vectors and invariant subspaces for the backward shift operator

R. G. Douglas; H. S. Shapiro; A. L. Shields — 1970

Annales de l'institut Fourier

The operator $U$ of multiplication by $z$ on the Hardy space $H^{2}$ of square summable power series has been studied by many authors. In this paper we make a similar study of the adjoint operator $U^{*}$ (the “backward shift”). Let $K_{f}$ denote the cyclic subspace generated by $f (f \in H^{2})$ , that is, the smallest closed subspace of $H^{2}$ that contains ${U^{* n} f}$ $(n \geq 0)$ . If $K_{f} = H^{2}$ , then $f$ is called a cyclic vector for $U^{*}$ . Theorem : $f$ is a cyclic vector if and only if there is a function $g$ , meromorphic and of bounded Nevanlinna characteristic...