We prove orthogonality relations for some analogs of trigonometric functions on a q-quadratic grid and introduce the corresponding q-Fourier series. We also discuss several other properties of this basic trigonometric system and the q-Fourier series.

We prove orthogonality relations for some analogs of trigonometric functions on a q-quadratic grid and introduce the corresponding q-Fourier series. We also discuss several other properties of this basic trigonometric system and the q-Fourier series.

Trigonometric non-isospectral flows are defined for KP hierarchy. It is demonstrated that symmetry constraints of KP hierarchy associated with these flows give rise to trigonometric Calogero-Moser system.

By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to statistical deviations of different magnitudes: (a) trigonometric; (b) hyperbolic; (c) hypertrigonometric. Each class is characterized by a perturbation of t...

Consider a plane curve given parametrically by a generalized trigonometric polynomial, that is, x + iy = P n k=1 a k e ik. In this paper, we obtain an impliciti-zation of the curve, that is, an equation in x and y which captures all the points on the curve and, if any, only nitely many more points.

Let G be any discrete Abelian group. We give several arithmetic characterizations of Sidon sets in G. In particular, we show that a set A is a Sidon set iff there is a number 6 > 0 such that any finite subset A of A contains a subset B Q A with |B| > 6\A\ which is quasiindependent, i.e. such that the only relation of the form ]C\eB e x ^ = '̂ with e\ equal to + 1 or 0, is the trivial one. Let G ...

for some nonnegative integer k and complex numbers a0, . . . , ak, b1, . . . , bk ∈ C. Trigonometric polynomials and their series counterparts, the Fourier series, play an important role in many areas of pure and applied mathematics and are likely to be quite familiar to the reader. When reflecting on the terminology, however, it is reasonable to wonder why the term trigonometric polynomial is ...

Let φ(n) be any function which grows more slowly than exponentially in n, i.e., limsup n→∞ φ(n)1/n ≤ 1. There is a double trigonometric series whose coefficients grow like φ(n), and which is everywhere convergent in the square, restricted rectangular, and one-way iterative senses. Given any preassigned rate, there is a one dimensional trigonometric series whose coefficients grow at that rate, b...