Backward Shift Operators on Bergman-Besov Spaces as Bergman Projections
Copyright policy )Backward Shift Operators on Bergman-Besov Spaces as Bergman Projections
Summary: We express backward shift operators on all Bergman-Besov spaces in terms of Bergman projections in one and several variables including the Banach function spaces and the special Hilbert spaces such as Drury-Arveson and Dirichlet spaces. These operators are adjoints of the shift operators and their definitions for the case \(p = 1\) and proper Besov spaces require the use of nontrivial imbeddings of the spaces into Lebesgue classes. Our results indicate that the backward shifts are compositions of imbeddings into Lebesgue classes followed by multiplication operators by the conjugates of the coordinate variables followed by Bergman projections on appropriate spaces. We apply our results to the wandering subspace property of invariant subspaces of the shift operators on certain of our Hilbert spaces.
backward shift operator, Bergman spaces and Fock spaces, Invariant subspaces of linear operators, Besov spaces and \(Q_p\)-spaces, Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces), Bergman spaces of functions in several complex variables, Drury-Arveson space, Bergman-Besov space, Hardy space, Bloch spaces, Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)), wandering subspace property, Dirichlet space, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Banach spaces of continuous, differentiable or analytic functions, Integral representations; canonical kernels (Szegő, Bergman, etc.), Bergman projection, Kernel operators, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), Hilbert spaces of continuous, differentiable or analytic functions
backward shift operator, Bergman spaces and Fock spaces, Invariant subspaces of linear operators, Besov spaces and \(Q_p\)-spaces, Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces), Bergman spaces of functions in several complex variables, Drury-Arveson space, Bergman-Besov space, Hardy space, Bloch spaces, Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)), wandering subspace property, Dirichlet space, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Banach spaces of continuous, differentiable or analytic functions, Integral representations; canonical kernels (Szegő, Bergman, etc.), Bergman projection, Kernel operators, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), Hilbert spaces of continuous, differentiable or analytic functions
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!