Related papers: Inversion of Separable Kernel Operators in Coupled…
The aim of this paper is to study time-fractional pseudo-parabolic type equations generated by the Dunkl operator. The forward problem is considered and its well-posedness is established. In particular, a prior estimates are obtained in the…
In this paper, for continuous, linearly-controllable quadratic control systems with a single input, an explicit, constructive method is proposed for studying their Brunovsky forms, initially studied in [W. Kang and A. J. Krener, Extended…
We introduce a new method to construct, within inverse-scattering theory, an energy-independent separable potential capable of reproducing exactly both phase shift and absorption over a predefined energy range. The approach relies on the…
We present an optimization-based framework for analysis and control of linear parabolic partial differential equations (PDEs) with spatially varying coefficients without discretization or numerical approximation. For controller synthesis,…
This paper presents a method for control synthesis under spatio-temporal constraints. First, we consider the problem of reaching a set $S$ in a user-defined or prescribed time $T$. We define a new class of control Lyapunov functions, called…
Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum…
Here Lq-Lp boundedness of integral operator with operator-valued kernels is studied and the main result is applied to convolution operators. Using these results Besov space regularity for Fourier multiplier operator is established.
In this paper we study closed subspaces of ultradifferentiable functions which are invariant under the differentiation operator. We propose a version of spectral synthesis which takes into account the presence of non-trivial differentiation…
We propose a counter-example guided inductive synthesis (CEGIS) scheme for the design of control Lyapunov functions and associated state-feedback controllers for linear systems affected by parametric uncertainty with arbitrary shape. In the…
We study the inverse dynamic problem of recoverying the potential in the one-dimensional dynamical system with memory. The Gelfand--Levitan equations are derived for the kernel of the integral operator which is inverse to the control…
In this technical report the $C_0$ semigroup of Frobenius-Perron operators on $L^1(X)$ is considered, where the underlying dynamical system is such that trajectories may leave the state space $X$ and terminate. We introduce a discrete…
The solution of a partial differential equation can be obtained by computing the inverse operator map between the input and the solution space. Towards this end, we introduce a \textit{multiwavelet-based neural operator learning scheme}…
Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of…
We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. We cast the Dynamic Mode-Decomposition type…
In the present paper, we consider the integral operator, which acts in Hilbert space and has sine kernel. This operator generates two operator identities and two corresponding canonical differential systems. We find the asymptotics of the…
We introduce an operator on problems in Weihrauch complexity, which we call the inverse limit, and which corresponds to an infinite compositional product. This operation arises naturally whenever one implements algorithms that produce a…
The integral operator of the form $$\bigl(Nu\bigr)(x)=\sum_{k=1}^\infty e^{i\langle\omega_k,x\rangle} \int_{\mathbb R^c}n_k(x-y)\,u(y)\,dy$$ acting in $L_p(\mathbb R^c)$, $1\le p\le\infty$, is considered. It is assumed that…
We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and…
This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…
In decentralized control problems, a standard approach is to specify the set of allowable decentralized controllers as a closed subspace of linear operators. This then induces a corresponding set of Youla parameters. Previous work has shown…