A Nonorthogonal Fourier Expansion for Conic Decomposition

We extend John's inscribed ellipsoid theorem, as well as Loewner's circumscribed ellipsoid theorem, from convex bodies to proper cones. To be more precise, we prove that a proper cone $$K$$K in $$\mathbb {R}^n$$Rn contains a unique ellipsoidal cone $$Q^\...

The following procedures are based on the Cooley-Tukey algorithm [1] for computing the finite Fourier transform of a complex data vector; the dimension of the data vector is assumed here to be a power of two. Procedure COMPLEXTRANSFORM computes either ...

The analysis of the mathematical structure of the integral Fourier transform shows that the transform can be split and represented by certain sets of frequencies as coefficients of Fourier series of periodic functions in the interval $$[0,2\pi)$$ . In this paper we ...