This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence of Padé approximants appears as the strong resolvent convergence of finite matrix approximations to a Jacobi matrix. As a bonus of this, we o...

This paper deals with the quantitative Schmidt's subspace theorem and general from of second main theorem, which are two correspondence objects in Diophantine approximation theory Nevanlinna theory. In this paper, we give a new below bound for Chow weight projective varieties defined over number field. Then, apply it to prove version polynomials higher degree subgeneral position respect variety...

In this paper, we prove a lemma on logarithmic derivative for holomorphic curves from annuli into K\"{a}hler compact manifold and. As its application, second main theorem holomophic semi abelian varieties intersecting with only one divisor is given.

A genericity condition is removed from a result of Agler and Young which reduces the spectral Nevanlinna-Pick problem in two dimensions to a family of classical Nevanlinna-Pick problems. Unlike the original approach, the argument presented here does not involve state-space methods.

It is shown how to study the 2-D Toda system for SU(n+1) using Nevanlinna theory of meromorphic functions and holomorphic curves. The results generalize recent results of Jost – Wang and Chen – Li. We consider the 2-dimensional open Toda system for SU(n + 1): − 2 ∆uj = −ej−1 + 2ej − ej+1, 1 ≤ j ≤ n, u0 = un+1 = 0, (1) where uj are smooth functions in the complex plane C, and n is a positive int...

We investigate the connections between Weyl–Titchmarsh– Kodaira theory for one-dimensional Schrödinger operators and the theory of n-entire operators. As our main result we find a necessary and sufficient condition for a one-dimensional Schrödinger operator to be nentire in terms of square integrability of derivatives (w.r.t. the spectral parameter) of the Weyl solution. We also show that this ...

We introduce a mean counting function for Dirichlet series, which plays the same role in theory of Hardy spaces series as Nevanlinna does classical theory. The existence is related to Jessen and Tornehave's resolution Lagrange motion problem. use describe all compact composition operators with symbols on Hardy--Hilbert space thus resolving problem has been open since bounded were described by G...

The Nevanlinna counting function is used to give several different characterizations of inner functions. The results all assert that a holomorphic selfmap of the unit disc is inner if and only if its Nevanlinna counting function is, in various pointwise, asymptotic, and operator-theoretic senses, as large as it can be. Although many of the results in this note are known, the asymptotic and oper...