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Refinable function. In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfils some kind of self-similarity. A function is called refinable with respect to the mask if. This condition is called refinement equation, dilation equation or two-scale equation . Using the convolution (denoted by a star, *) of a ...
The scaling function is a refinable function.That is, it is a fractal functional equation, called the refinement equation (twin-scale relation or dilation equation): = = (), ...
Transfer matrix. In applied mathematics, the transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable functions. Refinable functions play an important role in wavelet theory and finite element theory. For the mask , which is a vector with component indexes from to , the ...
Truncated power function. In mathematics, the truncated power function[ 1] with exponent is defined as. In particular, and interpret the exponent as conventional power .
A differentiable function. In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non- vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally ...
Category:Wavelets. Category. : Wavelets. Wikimedia Commons has media related to Wavelets. The theory of wavelets studies particular bases of function spaces, with a view to applications; they are a key tool in time–frequency analysis .
A Green's function, G(x,s), of a linear differential operator L = L(x) acting on distributions over a subset of the Euclidean space , at a point s, is any solution of. (1) where δ is the Dirac delta function. This property of a Green's function can be exploited to solve differential equations of the form.
In mathematics, a functional is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author). into the field of real or complex numbers. [ 2][ 3] In functional analysis, the term linear functional is a synonym of linear form; [ 3][ 4][ 5] that is, it is a scalar-valued linear map.