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The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.

Differential equations, Partial. --- Integral operators. --- Operators, Integral --- Integrals --- Operator theory --- Partial differential equations --- Boundary value problems. --- Spectral projection method. --- Spherical integral operator. --- Stochastic numeric.

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This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most of the contributions were originally presented at two conferences in Lisbon and Aveiro, Portugal, in June‒July 2011.

Harmonic analysis. --- Operator theory. --- Operator theory --- Harmonic analysis --- Integral operators --- Operator spaces --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematics. --- Potential theory (Mathematics). --- Potential Theory. --- Abstract Harmonic Analysis. --- Operator Theory. --- Functional analysis --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mechanics --- Samko, S. G. --- Samko, Stefan Grigorʹevich --- Samko, Stephan G.