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Symmetric Kernels and Orthogonal Systems of Functions
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analytic function approximation arbitrary constant asymptotic basic interval belongs Bessel functions boundary conditions Carleman class L2 consider convergent series corresponding deduced denotes determinant eigenfunctions eigenvalues existence fact finite follows formula Fourier coefficients Fredholm equation Fredholm integral equation ft=l given equation Green's formula Green's function Hence Hilbert-Schmidt theorem homogeneous equation hypothesis important infinite number infinite series instance iterated kernels kernel K(x L2-function L2-kernel L2-space linear combination linear differential equation linearly independent Math means membrane method Moreover non-homogeneous non-linear integral equation non-trivial solutions obtain ON-system orthogonal Parseval's equation polynomials previous section problem prove quadratically resolvent kernel respectively Riesz-Fischer theorem right-hand side satisfies condition Schwarz inequality second kind shows solved suitable symmetric kernel theory of integral transformation triangular kernel Tricomi uniformly convergent unknown function upper bound valid values vanish almost everywhere vanishes identically vibrations Volterra Equations Volterra integral equation zero