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Classiﬁcation of integral equations
7 other sections not shown
absolutely and uniformly abstract Hilbert space bounded linear operator Cauchy sequence characteristic functions characteristic value A1 complex numbers consider continuous functions convolution theorem convolution type corresponding degenerate kernel denoted differential equation element f example ﬁnd ﬁrst kind follows Fourier transforms Fredholm equation Fredholm integral equation function f(x function space given Greenís function Hermitian kernel Hilbert space inﬁnite series inner product iterated kemel kernel K(x kernel satisfying L2 functions Laplace transform linear differential linear integral equations linear integral operator linearly independent llfll llsll mathematical mean square convergent Mellin transform method of successive Neumann expansion Neumann series obtain orthogonal orthonormal system parameter Poissonís formula problem reciprocal formulae regular value resolvent equation right-hand side Schwarzís inequality second kind singular kernel square integrable function square integrable kernel square integrable solution successive approximations suppose symmetric kernel triangle inequality uniformly convergent vanishes veriﬁed Verify Volterra equation