Remarks on Inner Functions and Optimal Approximants Articles uri icon

publication date

  • December 2018

start page

  • 704

end page

  • 716

issue

  • 4

volume

  • 61

International Standard Serial Number (ISSN)

  • 0008-4395

Electronic International Standard Serial Number (EISSN)

  • 1496-4287

abstract

  • We discuss the concept of inner function in reproducing kernelHilbert spaces with an orthogonal basis of monomials and examine connections between inner functions and optimal polynomial approximants to 1/f , where f is a function in the space. We revisit some classical examples from this perspective, and show how a construction of Shapiro and Shields can be modiĆ»ed to produce inner functions.

keywords

  • inner function; reproducing kernel hilbert space; operator theoretic function theory