What is a Sobolev space for the Laguerre function systems?

• Autorzy: B. Bongioanni , J. L. Torrea
• Języki publikacji: EN

Abstrakty

EN

We discuss the concept of Sobolev space associated to the Laguerre operator $L_{α} = - y d²/dy² - d/dy + y/4 + α²/4y$, y ∈ (0,∞). We show that the natural definition does not agree with the concept of potential space defined via the potentials $(L_{α})^{-s}$. An appropriate Laguerre-Sobolev space is defined in order to achieve that coincidence. An application is given to the almost everywhere convergence of solutions of the Schrödinger equation. Other Laguerre operators are also considered.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 42C05: Orthogonal functions and polynomials, general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 192
• Numer: 2
• Strony: 147-172

Daty

wydano

2009

Twórcy

autor

B. Bongioanni

• Departamento de Matemática, Facultad de Ingeniería Qímica, Universidad Nacional del Litoral
• Instituto de Matemática Aplicada del Litoral, Santa Fe 3000, Argentina

autor

J. L. Torrea

• Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Identyfikatory

DOI

10.4064/sm192-2-4