110 citations · 337 across the 24 of their papers we have counts for
7 papers · 1 filter
Restricted Liouville Operator for the study of Non-Analytic Dynamics within the Disk
Sushant Pokhriyal, Joel A Rosenfeld
The study of Koopman and Liouville operators over reproducing kernel Hilbert spaces (RKHSs) has been gaining considerable interest over the past decade. In particular, these operat…
The kernel perspective on dynamic mode decomposition
Efrain Gonzalez, Moad Abudia, Michael Jury +2
This manuscript revisits theoretical assumptions concerning dynamic mode decomposition (DMD) of Koopman operators, including the existence of lattices of eigenfunctions, common eig…
Liouville Operators over the Hardy Space
Benjamin P. Russo, Joel A. Rosenfeld
The role of Liouville operators in the study of dynamical systems through the use of occupation measures have been an active area of research in control theory over the past decade…
Occupation Kernel Hilbert Spaces for Fractional Order Liouville Operators and Dynamic Mode Decomposition
Joel A. Rosenfeld, Benjamin Russo, Xiuying Li
This manuscript gives a theoretical framework for a new Hilbert space of functions, the so called occupation kernel Hilbert space (OKHS), that operate on collections of signals rat…
Introducing the Polylogarithmic Hardy Space
Joel A. Rosenfeld
In this paper we investigate the reproducing kernel Hilbert space where the polylogarithm appears as kernel functions. This investigation begins with the properties of functions in…
The Sarason Sub-Symbol and the Recovery of the Symbol of Densely Defined Toeplitz Operators over the Hardy Space
Joel Rosenfeld
While the symbol map for the collection of bounded Toeplitz operators is well studied, there has been little work on a symbol map for densely defined Toeplitz operators. In this wo…
Densely Defined Multiplication on the Sobolev Space
Joel A. Rosenfeld
Following Sarason's classification of the densely defined multiplication operators over the Hardy space, we classify the densely defined multipliers over the Sobolev space, $W^{1,2…