Approximation by polynomials in Sobolev spaces associated with classical moment functionals
Approximation by polynomials in Sobolev spaces associated with classical moment functionals
Abstract Let $$\textbf{u}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>u</mml:mi> </mml:math> be a moment functional associated with the Hermite, Laguerre, or Jacobi classical orthogonal polynomials. We study approximation by polynomials in $$H^r(\textbf{u})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mi>r</mml:mi> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>u</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , the Sobolev space consisting of functions whose …