The Krĕın-Langer integral representation of a matrix-valued generalized Nevanlinna function arises in problems of spectral theory and interpolation. A version of this formula which is suitable for such problems, and a corresponding Stieltjes inversion formula, are derived. Some classes of generalized Nevanlinna functions which are defined in terms of behavior at infinity are characterized in te...

An abstract Pick interpolation theorem for a family of positive semi-definite kernels on a set X is formulated. The result complements those in [Ag] and [AM02] and will subsequently be applied to Pick interpolation on distinguished varieties [JKM].

A natural interpolation problem in the cone of positive harmonic functions is considered and the corresponding interpolating sequences are geometrically described.

We introduce interpolation analogues of Schur Q-functions — the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-rows functions, vanishing and characterization properties, a Pieri-type formula, a Nimmo-type formula (a relation of two Pfaffians), a Giambelli-Schur-type Pfaffian formula, a determinantal formula...

We construct a Gaussian approximation to the effective theory for the Colour Glass Condensate which describes correctly the gluon distribution both in the low density regime at high transverse momenta (above the saturation scale Qs), and in the high density regime below Qs, and provides a simple interpolation between these two regimes. At high momenta, the effective theory reproduces the BFKL d...

Regional Gross Domestic Product Per Capita (GDP) GDP represents the regional GDP per capita measured as a proportion of the overall Spanish average of 100, adjusted annually. The regional GDP scores (along with the updated Spanish average of 100) were available for each of the 17 regions for 1973, 1985, 1989, 1991, and 1993. Missing years between 1977 and 1996 were given scores via interpolatio...

Abstract – Dynamic estimation of large-scale remote-sensing image sequences is important in a variety of scientific applications. However, the growing size of such sensed images makes conventional dynamic estimation methods, for example the Kalman and related filters, impractical. In this paper we present an approach that emulates the Kalman filter, but with considerably reduced computational a...