Transactions of the American Mathematical Society · 1963 · 118 citations · 3 references
Natural SciencesMathematicsPhysicsDifferential EquationsStochastic ProcessesEigenvalue ProblemsIntegral Equation FormulationsIntegral EquationsSpectral TheoryAsymptotic TheoryEigenfunction ExpansionsEigenvalue Problems For Integral EquationsSpectral AsymptoticsSturm - Liouville Theory
then To is just convolution by k. However we shall not insist that this be the case. Let V(x) be a bounded non-negative function with bounded support and denote by MVI/2 the operator on L2(Ed) which is multiplication by V(x)1/2. We shall denote by 21 > A2 _> ? the positive eigenvalues of the positive semi-definite operator MVl/2ToMvI/2. In case K is the Fourier transform of an L1 function k then this is just the integral operator in equation (1).The result (Theorem II) is as
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Ordinary Differential Equations
A. T. Lonseth, E. L. Ince · National Mathematics Magazine · 1945 · 3.2K citations