45A05 Linear integral equations

Overview

45A05 treats linear integral equations within linear integral equations. Typical questions involve existence, uniqueness, representation formulas, inversion, and stability of solution operators in analytic and applied settings.

Related Wikipedia Page

Wikipedia search: Linear integral equations

Useful Links

• Wikipedia search: Linear integral equations
• Encyclopaedia of Mathematics
• arXiv: Classical Analysis and ODEs (math.CA)
• Journal of Integral Equations and Applications
• Integral Equations and Operator Theory
• Journal of Mathematical Analysis and Applications

Key Ideas

• Canonical formulations and operator-theoretic viewpoints for linear integral equations
• Kernel properties, transform methods, and regularity assumptions
• Analytic and numerical criteria for solvability and stability

Typical Uses

Used to reformulate differential and boundary-value models as operator equations, derive qualitative properties of solutions, and support approximation schemes.

Applications

• Potential theory, wave/heat propagation, and inverse-problem modeling
• Numerical simulation pipelines where integral formulations improve conditioning
• Systems and control contexts using convolution and memory-type operators

References

• Tricomi, F.G. (1985) Integral Equations. New York, NY: Dover Publications.
• Kress, R. (2014) Linear Integral Equations. 3rd edn. New York, NY: Springer.
• Mikhlin, S.G. (1957) Integral Equations. Oxford: Pergamon Press.

Recommended Textbooks

• Kress, R. (2014) Linear Integral Equations. 3rd edn. New York, NY: Springer.
• Tricomi, F.G. (1985) Integral Equations. New York, NY: Dover Publications.
• Mikhlin, S.G. (1957) Integral Equations. Oxford: Pergamon Press.