Abstract
In this study, we employ new results on the semi‐inner product, the adjoint operator, and the Schatten class of operators on a separable Banach space, which allow us to investigate a differential operator with unbounded operator‐valued coefficients. Specifically, we derive an asymptotic formula for the second regularized trace based on the asymptotic and spectral properties of the extended operator. For this purpose, we use the theory of continuous dense embeddings and known results regarding the regularized trace in Hilbert space. We conclude our paper by providing examples that support our findings.
Keywords
Mathematics
Separable space
Banach space
Regularization (linguistics)
TRACE (psycholinguistics)
C0-semigroup
Differential operator
Finite-rank operator
Mathematical analysis
Trace operator
Approximation property
Pseudo-monotone operator
Compact operator
Applied mathematics
Pure mathematics
Operator space
Extension (predicate logic)
Boundary value problem
Elliptic boundary value problem
Free boundary problem
Computer science
Subject Areas
Numerical methods in inverse problems
·Mathematical Physics ·Physical Sciences
Differential Equations and Boundary Problems
·Applied Mathematics ·Physical Sciences
Advanced Mathematical Modeling in Engineering
·Computational Theory and Mathematics ·Physical Sciences
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