A note on the p-adic Kozyrev wavelets basis

• Autores: Edilberto Arroyo Ortiz
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 55, Nº. 1, 2021, págs. 1-12
• Idioma: inglés
• DOI: 10.15446/recolma.v55n1.99095
• Títulos paralelos:
  • Una nota sobre la base de Kozyrev de wavelets p− ádicos
• Enlaces
  • Texto completo
• Resumen
  • español

    Presentamos una base de wavelets p− ádica para espacios de tipo Sobolev que consiste de vectores propios de ciertos operadores pseudodiferenciales. Nuestro resultado extiende un conocido resultado debido a S. Kozyrev.

  • English

    We present a basis of p−adic wavelets for Sobolev-type spacesconsisting of eigenvectors of certain pseudodifferential operators. Our resultextends a well-known result due to S. Kozyrev.

• Referencias bibliográficas
  • S. Albeverio, A. Yu. Khrennikov, and V. M. Shelkovich, Theory of p-adic distributions: linear and nonlinear models, Cambridge University Press,...
  • S. Albeverio and S. V. Kozyrev, Multidimensional basis of p-adic wavelets and representation theory, p-Adic Numbers Ultrametric Anal. Appl...
  • E. Arroyo-Ortiz and W. A. Zu~niga-Galindo, Construction of p-adic covariant quantum elds in the framework of white noise analysis, Reports...
  • L. Brekke, P. G. O. Freund, M. Olson, and E. Witten, Nonarchimedean string dynamics, Nucl. Phys B302 (1988), no. (3), 365-402.
  • A. Yu. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer Academics, Dordrecht, 1997.
  • A. Yu. Khrennikov, S. V. Kozyrev, and W. A. Zúñiga-Galindo, Ultrametric Equations and its Applications, Encyclopedia of Mathematics and its...
  • M. H. Taibleson, Fourier analysis on local fields, Princeton University Press, 1975.
  • V. S. Varadarajan, Non-archimedean models for space-time, Modern Phys. Lett. A 16 (2001), no. 4-6, 387-395.
  • V. S. Vladimirov, On the equations for p-adic closed and open strings, p-Adic Numbers Ultrametr. Anal. Appl. 1 (2009), no. 1, 79-87.
  • V. S. Vladimirov and I. V. Volovich, p-adic quantum mechanics, Comm. Math. Phys. 123 (1989), no. 4, 659-676.
  • V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, Spectral theory in p-adic quantum mechanics and representation theory, Mathematics of...
  • V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, p-adic analysis and mathematical physics, Series On Soviet And East European Mathematics,...
  • I. V. Volovich, p-adic string, Clas. Quant. Gravity 4 (1987), no. 1, L83-L87.
  • I. V. Volovich, Number theory as the ultimate physical theory, p-Adic Numbers Ultrametr. Anal. Appl. 2 (2010), no. 1, 77-87.
  • W. A. Zúñiga-Galindo, Pseudodifferential equations over non-archimedean spaces, Lectures Notes in Mathematics, Springer, 2016.
  • W. A. Zúñiga-Galindo, Non-archimedean white noise, pseudodifferential stochastic equations, and massive euclidean fields, J. Fourier Anal....