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The Fourier sine transform is the imaginary part of the full complex Fourier transform, F_x^((s))[f(x)](k) = I[F_x[f(x)](k)] (1) = int_(-infty)^inftysin(2pikx)f(x)dx. (2) The ...

Let Omega be an open, bounded, and connected subset of R^d for some d and let dx denote d-dimensional Lebesgue measure on R^d. In functional analysis, the Friedrichs ...

The Gelfand transform x|->x^^ is defined as follows. If phi:B->C is linear and multiplicative in the senses phi(ax+by)=aphi(x)+bphi(y) and phi(xy)=phi(x)phi(y), where B is a ...

An apodization function, also called the Hann function, frequently used to reduce leakage in discrete Fourier transforms. The illustrations above show the Hanning function, ...

The simplest interpretation of the Kronecker delta is as the discrete version of the delta function defined by delta_(ij)={0 for i!=j; 1 for i=j. (1) The Kronecker delta is ...

The Legendre transform of a sequence {c_k} is the sequence {a_k} with terms given by a_n = sum_(k=0)^(n)(n; k)(n+k; k)c_k (1) = sum_(k=0)^(n)(2k; k)(n+k; n-k)c_k, (2) where ...

A Lie group is a group with the structure of a manifold. Therefore, discrete groups do not count. However, the most useful Lie groups are defined as subgroups of some matrix ...

A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief ...

The longest increasing scattered subsequence is the longest subsequence of increasing terms, where intervening nonincreasing terms may be dropped. Finding the largest ...

A meromorphic function is a single-valued function that is analytic in all but possibly a discrete subset of its domain, and at those singularities it must go to infinity ...