45P05 Integral operators

Overview

45P05 studies integral operators in the setting of integral equations in abstract spaces. Emphasis is placed on solvability, regularity, operator structure, and computationally stable representations for deterministic or stochastic models.

Related Wikipedia Page

Wikipedia: Integral operator

Useful Links

• Wikipedia: Integral operator
• Encyclopaedia of Mathematics
• arXiv: Classical Analysis and ODEs (math.CA)
• Integral Equations and Operator Theory
• Journal of Functional Analysis
• Studia Mathematica

Key Ideas

• Model-specific formulation of integral operators and associated kernels/operators
• Existence, uniqueness, and continuity under analytic or probabilistic assumptions
• Connections between theoretical criteria and practical approximation schemes

Typical Uses

Used to analyze memory effects, inverse formulations, and structured boundary phenomena where integral operators provide natural model representations.

Applications

• Physics and engineering models with hereditary or nonlocal interactions
• Stochastic and uncertainty-aware formulations in applied analysis
• Computational frameworks for inverse and parameter-identification problems

References

• Aleksandrov, A.B. and Peller, V.V. (2002) Distorted Hankel integral operators. arXiv:0212293v1.
• Google Scholar (PDF results): Aleksandrov, A.B. and Peller, V.V. (2002) Distorted Hankel integral operators. arXiv:0212293v1.

Recommended Textbooks

• Zeidler, E. (1986) Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems. New York, NY: Springer. — Amazon · Bookshop.org
• Conway, J.B. (1990) A Course in Functional Analysis. 2nd edn. New York, NY: Springer. — Amazon · Bookshop.org
• Kress, R. (2014) Linear Integral Equations. 3rd edn. New York, NY: Springer. — Amazon · Bookshop.org