On infinitely smooth almost-wavelets with compact support

• Autores: M. Berkolaiko, S. Ya. Novikov
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 44, Fasc. 1-3, 1993, págs. 41-46
• Idioma: inglés
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• Resumen

  • 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