Liouville–weyl derivatives, best approximations, and moduli of smoothness

• Autores: Ainur Jumabayeva
• Directores de la Tesis: Sergey Tikhonov (dir. tes.)
• Lectura: En la Universitat Autònoma de Barcelona ( España ) en 2018
• Idioma: español
• Tribunal Calificador de la Tesis: Elijah Liflyand (presid.), Joaquim Martín Pedret (secret.), Yurii Kolomoitsev (voc.)
• Programa de doctorado: Programa de Doctorado en Matemáticas por la Universidad Autónoma de Barcelona
• Materias:
  • Matemáticas
    • Análisis y análisis funcional
      • Teoría de la aproximación
      • Análisis armónico
• Enlaces
  • Tesis en acceso abierto en:  TESEO  TDX 
• Resumen

  • This work is devoted to the study of approximation and smoothness properties of the generalized Liouville-Weyl derivatives. The main three problems we address are the following.

    First, we obtain new upper and lower estimates of norms and best approximations of the generalized Liouville-Weyl derivatives in terms of the best approximations of functions themselves. To deal with Liouville-Weyl derivatives, we make use of the concept of general monotonicity.

    Second, we study a similar problem for moduli of smoothness of fractional order. More specifically, we prove new inequalities for moduli of smoothness of the generalized Liouville-Weyl derivatives via moduli of smoothness of functions themselves.

    Both problems can be naturally divided into two cases: Lp-Lp and Lp-Lq estimates.

    Third, we obtain new inequalities for best approximations by angle in the multivariate case.