Resumen de On infinitely smooth almost-wavelets with compact support

M. Berkolaiko, S. Ya. Novikov

• In 1985 Y. Meyer has constructed the infinitely smooth function $\psi(t), t\in\mathbb{R}$, with compact spectrum such that the system of functions $2^{\frac{j}{2}}\psi(2^jt-k), j,k\in\mathbb{Z}$, forms an orthonormal basis for $L_2(\mathbb{R})$ [1]. Now such systems are called wavelets. There are known wavelets with exponential decay on infinity [2,3,4] and wavelets with compact support [5]. But these functions have finite smoothness. It is known that there does not exist infinitely differentiable compactly supported wavelets