ABSTRACT
Let μ be a measure on the extended real line ℝ ^ = ℝ ∪ { ∞ } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072126/15070696-a94f-4da5-a117-8ee069a896b3/content/eq1078.tif"/> . Its Nevanlinna transform is defined as Ω μ ( z ) = ∫ D ( t , z ) d μ ( t ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072126/15070696-a94f-4da5-a117-8ee069a896b3/content/eq1079.tif"/> with D(t, z) = i(1 + tz)/(z − t). It is a holomorphic function in the upper half plane with nonnegative real part. In this paper we construct rational approximants Ω n (z) of degree n, which belong to the same class and are such that for an arbitrary sequence of points α k ∈ ℝ ^ , k = 1 , 2 , … https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072126/15070696-a94f-4da5-a117-8ee069a896b3/content/eq1080.tif"/> , we have Hermite interpolation at these points for the boundary functions of Ω μ and Ω n . This means that the nontangential limits of Ω μ − Ω n and an appropriate number of its derivatives vanish in the given points αk .
Keywords: orthogonal rational functions, rational interpolation.
AMS Classification: 30E05, 30E15, 41A20
