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 31by J.M. Cowley - 1995 - 488 pagesLimited preview - About this book
| 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... | |
| 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... | |
| 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... | |
| Eberhard Freitag, Rolf Busam - Mathematics - 2005 - 574 pages
...involved powers NI,..., Nm. Using V.3.1, g(z) is a polynomial in p(z), and we are done. D Any elliptic **function can be written as a sum of an even and an odd function,** both elliptic: because together with z i—> f(z) also z \^ f(-z) is an elliptic function. Let's look... | |
| David L. Powers - Mathematics - 2006 - 516 pages
...interval. Most functions are neither even nor odd, but any function that is defined on a symmetric interval **can be written as a sum of an even and an odd function: f(x)** = It is easy to show that the first term is an even function and the second is odd. Even and odd functions... | |
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