Analytic Theory of a Class of Interpolation Problems

Abstract

Specific heat measurements have been made between 0.2 and 4 K on NdNi,, NdAl, and NdCo, and also on LaA1,. Hyperfine contributions have been identified in the neodymium compounds, and the ionic moments deduced, giving 1.63 pB, 2.39 pB and 2.63 pB respectively. These moments, the known Curie temperatures and paramagnetic susceptibilities, can all be interpreted in terms of a common model to represent crystal field and exchange effects. All three compounds have 'electronic' specific heats which are far larger than the electronic specific heat of LaA1, ( y = 12.1 mJ mole-' K -2 ) .

On degenerate interpolation, entropy and extremal problems for matrix Schur functions

“…Although the inequalities (3.4) and (4.7) are equivalent, their simultaneous use seems to be convenient and fruitful; for applications to concrete interpolation problems see [12] and [26].…”

On rank variation of block matrices generated by Nevanlinna matrix functions

“…In the case of m = 1 and ξ 1 = z, we obtain a so-called Fundamental Matrix Inequality: H (τ,p,p ) n,m ≥ 0, which plays an important role in the Potapov theory of moment problems (see [11]). For m ≥ 1, the matrix H (τ,p,p ) n,m does coincide with a generalized block Pick-like matrix of a certain matrix version of Akhieser problem (see [1,14]).…”

Tangential Nevanlinna-Pick Interpolation and Its Connection with Hamburger Matrix Moment Problem

“…The Nevanlinna-Pick interpolation and moment problem have been widely studied in the literature, and interconnections between these two types of interpolation problems are well recognized (see, e.g., the monographs [Akh,KrN1,BGR,FoF,Dym] and the references therein, and [KrN2,Nud1,Nud2,Kov,IvS,Sar,Bol1,Bol2,Che,ChL,ChH1,ChH2], etc. for more information).…”