arXiv subjects

Sushant Pokhriyal

Publications and source records attributed to Sushant Pokhriyal.

4 recordsLinked to original sources

arXiv2026

Integral Formulation of QENDy for Robust Nonlinear System Identification

This manuscript proposes an integral formulation of the newly defined quadratic embedding method for identifying nonlinear systems (QENDy). In the original algorithm, trajectory data points along with their time derivatives are used. Methods for calculating time derivatives make the algorithm sensitive to noise. Our integral formulation does not use the time derivatives. This results in a more robust method to learn the dynamics.

math.DS↗

arXiv2025

Restricted Liouville Operator for the study of Non-Analytic Dynamics within the Disk

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 operators represent nonlinear dynamical systems, and through the study of these operators, methods of system identification and approximation can be derived through the exploitation of the linearity of these systems. The resulting algorithms, such as Dynamic Mode Decompositions, can then make predictions about the finite-dimensional nonlinear dynamics through a linear model in infinite dimensions. However, considering bounded and densely defined Koopman and Liouville operators over RKHSs often restricts the dynamics to those whose smoothness or analyticity matches that of the functions within that space. To circumvent this limitation, this manuscript introduces the Restricted Liouville Operator over the Hardy space on unit disc, which will allow for a wider class of dynamics (non-analytic or non-smooth) than available.

math.FA↗

arXiv2022

Invariant subspaces of powers of some unicellular operators

In this paper we study subspaces which are invariant under squares and cubes (separately as well as jointly) of unicellular backward weighted shift operators on a separable Hilbert space. The finite-dimensional subspaces are characterized for all weights and the infinite-dimensional subspaces are characterized for two classes of weights.

math.FA↗

arXiv2022

Multivariable Sub-Hardy Hilbert Spaces Invariant under the action of $n$-tuple of Finite Blaschke factors

This paper deals with representing in concrete fashion those Hilbert spaces that are vector subspaces of the Hardy spaces $H^p(\bb D^n) \ (1\le p\le \infty)$ that remain invariant under the action of coordinate wise multiplication by an $n$-tuple $(T_{B_1},\dots, T_{B_n})$ of operators where each $B_i, \ 1\le i\le n,$ is a finite Blaschke factor on the open unit disc. The critical point to be noted is that these $T_{B_i}$ are assumed to be weaker than isometries as operators. Thus our main theorem extends the principal result of \cite{LS} in the following three directions: $(i)$ from one to several variables; $(ii)$ from multiplication with the coordinate function $z$ to an $n$-tuple of multiplication by finite Blaschke factors $B_i, \ 1\le i\le n;$ $(iii)$ from vector subspaces of $H^2(\bb D)$ to the case of vector subspaces of $H^p(\bb D^n), \ 1\le p\le \infty.$ We further derive a generalization of Slocinski's well known Wold type decomposition of a pair of doubly commuting isometries to the case of $n$-tuple of doubly commuting operators whose actions are weaker than isometries.

math.FA↗