Double cosine-sine series and Nikol'skii classes in uniform metric

Uniform convergence of single and double sine series and integrals

Double Sine Series and Higher Order Lipschitz Classes of Functions (communicated by Hüseyin Bor)

Let ω(h, k) be a modulus of continuity, that is, ω(h, k) is a continuous function on the square [0, 2π] × [0, 2π], nondecreasing in each variable, and possessing the following properties: ω(0, 0) = 0, ω(t1 + t2, t3) ≤ ω(t1, t3) + ω(t2, t3), ω(t1, t2 + t3) ≤ ω(t1, t2) + ω(t1, t3). Yu ([3]) introduced the following classes of functions: HH := {f(x, y) : ‖f(x, y)− f(x+ h, y)− f(x, y + k) + f(x+ h,...

Discrete Cosine and Sine Transforms

Local Sine and Cosine Bases

19 and = 1 + 1 m ; m a positive integer. If we let w(x) 1 p 2 R 1 ?1 e ixx ()dd, then w is a \mother function" that generates a wavelet basis (giving us a Multi Resolution Analysis) m ; m a positive integer. x6. Concluding remarks. We repeat that the local bases we developed in x2. were introduced by Coifman and Meyer, and their use in obtaining the smooth wavelet bases were pointed out to us b...

Fractional Cosine and Sine Transforms

The fractional cosine and sine transforms – closely related to the fractional Fourier transform, which is now actively used in optics and signal processing – are introduced and their main properties and possible applications are discussed.