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CONCEPT OF A FOURIER SERIES
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absolutely integrable analogous approximated assumptions of Theorem boundary conditions bounded variation calculation called Cauchy sequence Chapter complete and orthogonal complete orthogonal systems complex numbers consequently considered constant converges uniformly Denote differential equation easily verify eigenfunctions element Example exists expansion fact find the Fourier finite interval finite number fk(x fN(x formal formula Fourier coefficients Fourier series Fourier transform function f(x given Hence Hilbert space Hint inequality initial conditions integrable function kernel Lebesgue Lebesgue integrable Let the function limit non-negative norm nx dx obtain orthonormal system Parseval's equality partial sums period 2n periodic function periodic with period periodically extended proof of Theorem properties prove real number Remark respect right hand side scalar product Section series converges space H space L2(a string substitution term by term trigonometric polynomial trigonometric series uniformly convergent vanish variable vectors