Integral Equations

a₁ absolutely and uniformly abstract Hilbert space bounded linear operator CALIFORNIA/SANTA CRUZ UNIVERSITY Cauchy sequence characteristic functions characteristic values complex numbers consider continuous functions convolution theorem convolution type CRUZ The University defined degenerate kernel differential equation example fn(x follows Fourier transforms Fredholm equation Fredholm integral equation functions f(x Green's function Hence Hermitian kernel Hilbert space K₁(x kernel K(x kernel satisfying Kn(x Laplace transform linear integral equations linear integral operator linearly independent mean square convergent Mellin transform Neumann expansion Neumann series obtain orthogonal orthonormal system problem regular value resolvent equation right-hand side Schwarz's inequality second kind singular kernel square integrable function square integrable kernel square integrable solution suppose symmetric kernel triangle inequality uniformly convergent University Library UNIVERSITY UNIVERSITY OF CALIFORNIA/SANTA vector Verify Volterra equation zero δφ λ₁ λε Σ Σ дх