This paper presents In-Context Operator Networks (ICON), a neural network approach that can learn new operators from prompted data during the inference stage without requiring any weight updates.

SIAM Journal on Applied Mathematics, Vol. 42, No. 5 (Oct., 1982), pp. 941-955 (15 pages) Slepian, Landau and Pollak found that a certain finite convolution integral operator on the real line commutes ...

Inverse problems in spectral theory address the challenge of reconstructing differential operators from observed spectral data. This field, rich in both theoretical and applied mathematics, underpins ...

Department of Mathematical Sciences, Yeshiva University, New York, USA. Shandong Iron and Steel Company Ltd., Jinan, China. The State Key Laboratory of Tribology, Tsinghua University, Beijing, China.

Inverse problems in differential operators and spectral theory constitute a vibrant research area where one seeks to determine unknown parameters within differential equations from observed spectral ...

Abstract: Using Walsh functions the solution of a linear periodic delay differential equation is approximated. The monodromy operator is then constructed based in the solution obtained. Dominant ...

ABSTRACT: In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three ...

Neural networks have been widely used to solve partial differential equations (PDEs) in different fields, such as biology, physics, and materials science. Although current research focuses on PDEs ...

In this work, we find the asymptotic formulas for the sum of the negative eigenvalues smaller than −ε (ε > 0) of a self-adjoint operator L defined by the following differential expression ℓ(y) = −(p(x ...