Notations

		Fourier translation of function f:
F		Fourier transform
F		Inverse Fourier transform
		Space integrable function on
		Space of square integrable functions over or set of finite energy signals over
(, )		Scalar product in space
_{L ²}		Norm in space
		Space of square-summable sequences indexed by
		Set of continuous functions over
		Set of n times continuously differentiable functions over
		Set of rapidly decreasing indefinitely differentiable functions over
		Dual space of ; set of tempered distributions over
C _n ^k		Binomial coefficients for 0 ? k ? n
V		Closure of set V (the smaller closed subspace containing V)
V ? W		Direct sum of spaces V and W; set of elements of the form v + w with v ? V and w ? W
V ? W		Spaces V and W are orthogonal
z		Complex conjugate number of
?		White noise
?		Dirac distribution (at point 0)
V _j		Space of approximations at level j
W _j		Space of details at level j
A _j or A ^j		Approximation at level j (reconstructed in V ₀)
D _j or D ^j		Detail at level; (reconstructed in V ₀)
?		Wavelet associated with a multiresolution analysis (discrete analysis) or satisfying the admissibility condition (continuous analysis)
? _a,b