Integral EquationsFor graduate students and applied mathematicians. |
Contents
1 | 11 |
L₂Kernels and Functions | 11 |
Volterra Equations of the First Kind | 15 |
Copyright | |
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already applied approximation arbitrary assume basic interval becomes belongs boundary bounded called class L₂ closed coefficients complete condition Consequently consider constant continuous converges corresponding deduced denotes determinant differential equation difficult eigenfunctions eigenvalues equality everywhere example existence fact finite follows formula Fourier Fredholm integral equation function f(x given gives Hence identically immediately important independent inequality instance integral equation kernel K(x L₂-function least limit linear means method Moreover necessarily non-linear observe obtain obviously ON-system orthogonal particular polynomials positive previous section problem proof prove reduced resolvent kernel respectively satisfies second kind shows side similar simple solution solved successive sufficient suitable symmetric kernel theorem theory transformation uniformly unique unknown valid values vanishes Volterra integral equation write zero