Finite Dimensional Backward Shift Invariant Subspaces of a Class of Reproducing Kernel Hilbert Spaces

2004 ◽  
Vol 52 (5) ◽  
pp. 321-334 ◽  
Author(s):  
V. Bolotnikov ◽  
L. Rodman †
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Invariant Subspaces ◽  
Reproducing Kernel Hilbert Spaces ◽  
Finite Dimensional ◽  
Backward Shift ◽  
Kernel Hilbert Spaces

scholarly journals Backward shift invariant subspaces in reproducing kernel Hilbert spaces

2020 ◽  
Vol 126 (1) ◽  
pp. 142-160
Author(s):  
Emmanuel Fricain ◽  
Javad Mashreghi ◽  
Rishika Rupam
Keyword(s):  
Hilbert Spaces ◽  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Bergman Spaces ◽  
Invariant Subspaces ◽  
Extreme Case ◽  
Reproducing Kernel Hilbert Spaces ◽  
Backward Shift ◽  
Kernel Hilbert Spaces ◽  
New Applications

In this note, we describe the backward shift invariant subspaces for an abstract class of reproducing kernel Hilbert spaces. Our main result is inspired by a result of Sarason concerning de Branges-Rovnyak spaces (the non-extreme case). Furthermore, we give new applications in the context of the range space of co-analytic Toeplitz operators and sub-Bergman spaces.

INDEFINITE KERNEL NETWORK WITH DEPENDENT SAMPLING

2013 ◽  
Vol 11 (05) ◽  
pp. 1350020 ◽  
Author(s):  
HONGWEI SUN ◽  
QIANG WU
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Function Class ◽  
Positive Definiteness ◽  
Reproducing Kernel Hilbert Spaces ◽  
Strong Mixing ◽  
Mixing Condition ◽  
Indefinite Kernel ◽  
Learning Rates ◽  
Kernel Hilbert Spaces

We study the asymptotical properties of indefinite kernel network with coefficient regularization and dependent sampling. The framework under investigation is different from classical kernel learning. Positive definiteness is not required by the kernel function and the samples are allowed to be weakly dependent with the dependence measured by a strong mixing condition. By a new kernel decomposition technique introduced in [27], two reproducing kernel Hilbert spaces and their associated kernel integral operators are used to characterize the properties and learnability of the hypothesis function class. Capacity independent error bounds and learning rates are deduced.

scholarly journals Scattering Systems with Several Evolutions and Formal Reproducing Kernel Hilbert Spaces

2014 ◽  
Vol 9 (4) ◽  
pp. 827-931 ◽  
Author(s):  
Joseph A. Ball ◽  
Dmitry S. Kaliuzhnyi-Verbovetskyi ◽  
Cora Sadosky ◽  
Victor Vinnikov
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Spaces ◽  
Kernel Hilbert Spaces ◽  
Scattering Systems
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