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This is a generalization of the very simple statement that any arbitrary function can be written as a sum of an even and an odd function...
Diffraction Physics - Page 31
by J.M. Cowley - 1995 - 488 pages

## Abstract Algebra with Applications: Volume 1: Vector Spaces and Groups

Karlheinz Spindler - Mathematics - 1993 - 780 pages
...all odd functions are clearly subspaces of T. We claim that Т = ,Feven 0 Fodd. In fact, an arbitrary function / can be written as a sum of an even and an odd function; namely, / = /t+/2 where /,(z) := \(f(x)+f(-x)) and/2(x) := |(/(x)-/(-x)). On the other hand, if / is...

## Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics

W.-H. Steeb - Science - 1998 - 256 pages
...function. Proof. at Remark. The same holds for odd functions. Theorem. An arbitrary function u can always be written as a sum of an even and an odd function. Proof. Using the identity _ 1 1 we find that u(q) + u(-q) is an even function and u(q) - u(-q) is an...

## Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography

Earl G. Williams - Mathematics - 1999 - 324 pages
...Fourier transform of f(x) with even and odd parts given by E and O, respectively, then Note that e~tk*x can be written as a sum of an even and an odd function in x. 1.4 Write the convolution theorem for ^ /j^ F(kx)G(kx)H(kx)eik'xdkx. 1.5 The zero-order Hankel...