Abstract This paper is concerned with description of the existence and forms entire solutions several second-order partial differential-difference equations more general Fermat type. By utilizing Nevanlinna theory meromorphic functions in complex variables we obtain some results on for these equations, which are extensions generalizations previous theorems given by Xu Cao (Mediterr. J. Math. 15...

We study the Nevanlinna-Pick problem for a class of subalgebras of H∞. This class includes algebras of analytic functions on embedded disks, the algebras of finite codimension in H∞ and the algebra of bounded analytic functions on a multiply connected domain. Our approach uses a distance formula that generalizes Sarason’s [18] work. We also investigate the difference between scalar-valued and m...

It is proved that the Riemann zeta function does not satisfy any nontrivial algebraic difference equation whose coefficients are meromor-phic functions φ with Nevanlinna characteristic satisfying T (r, φ) = o(r) as r → ∞.

The abstract interpolation problem (AIP) in the Schur class was posed V. Katznelson, A. Kheifets and P. Yuditskii in 1987 as an extension of the V.P. Potapov’s approach to interpolation problems. In the present paper an analog of the AIP for Nevanlinna classes is considered. The description of solutions of the AIP is reduced to the description of L-resolvents of some model symmetric operator as...

We introduce the notion of a Λ-nonisotropically balanced domain and show that the symmetrized polydisc in Cn, n ≥ 2, is an example of such a domain. Given a Λ-nonisotropically balanced domain Ω, we derive effective estimates from above and from below for the Lempert function κ̃Ω at (0, z) ∈ Ω × Ω. We use these estimates to derive certain conditions for realising a two-point Nevanlinna-Pick inter...

Let E , E∗ be Hilbert spaces. Given a Hilbert space H of holomorphic functions in a domain Ω in C, consider the multiplier space MH(E , E∗). It is shown that for “nice enough” H, the following statements are equivalent for f ∈ MH(E , E∗): (1) There exists a g ∈ MH(E∗, E) such that g(z)f(z) = IE for all z ∈ Ω. (2) There exists a Hilbert space Ec and fc ∈ MH(Ec, E∗) such that F (z) := [ f(z) fc(z...