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What is a Sobolev space for the Laguerre function systems?

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Bongioanni B., Torrea J.

Studia Mathematica

2009

tom 192

nr 2

147-172

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.

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1 Studia Mathematica

1 Bongioanni B.

1 Torrea J.

1 2009

Wyniki wyszukiwania

What is a Sobolev space for the Laguerre function systems?