Pick interpolation for a uniform algebra
Podal subspaces on the unit polydisk
Beurling's classical theorem gives a complete characterization of all invariant subspaces in the Hardy space H²(D). To generalize the theorem to higher dimensions, one is naturally led to determining the structure of each unitary equivalence (resp. similarity) class. This, in turn, requires finding podal (resp. s-podal) points in unitary (resp. similarity) orbits. In this note, we find that H-outer (resp. G-outer) functions play an important role in finding podal (resp. s-podal) points. By the methods...
Point derivations and prime ideals in R(X)
Pointwise multiplication operators on weighted Banach spaces of analytic functions
For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator , , on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map .
Principalité des idéaux de type fini de
Projections on Hardy spaces in the Lie ball.
On the Lie ball w of Cn, n ≥ 3, we prove that for all p ∈ [1,∞), p ≠ 2, the Hardy space Hp(w) is an uncomplemented subspace of the Lebesgue space Lp(∂0w, dσ), where ∂0w denotes the Shilov boundary of w and dσ is a normalized invariant measure of ∂0w.
Projective Lie Algebra Bases of a Locally Compact Group and Uniform Differentiability.
Propriétés spectrales en analyse non archimédienne
Pseudo-uniform Convexity in Hardy Spaces over Riemann Surfaces.
Pseudo-Uniform Convexity of the Hardy Class H on Riemann Surfaces.