Sobolev orthogonal polynomials on product domains Articles uri icon

publication date

  • August 2015

start page

  • 202

end page

  • 215

volume

  • 284

international standard serial number (ISSN)

  • 0377-0427

electronic international standard serial number (EISSN)

  • 1879-1778

abstract

  • Orthogonal polynomials on the product domain [a(1), b(1)] x [a(2), b(2)] with respect to the inner product < f, g >(s) = integral(b1)(a1) integral(b2)(a2) del f(x, y) center dot del g(x, y) w(1)(x)w(2)(y) dx dy +lambda f(c(1), c(2))g(c(1), c(2)) are constructed, where w(i) is a weight function on [a(i), b(i)] for i = 1, 2, lambda > 0, and (c(1), c(2)) is a fixed point. The main result shows how an orthogonal basis for such an inner product can be constructed for certain weight functions, in particular, for product Laguerre and product Gegenbauer weight functions, which serve as primary examples.