Explore the vast range of titles available.

We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs

We investigate the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least For real weights that are not an integer at least A tool in establishing these results is the relation to cohomology groups with values in modules of “analytic boundary germs”, which are represented by harmonic functions on subsets of the upper half-plane. It turns out that for integral weights at least

In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family SWΣ(δ,γ,λ,s,t,q,r) of normalized holomorphic and bi-univalent functions in the open unit disk U, which are associated with the Bazilevič functions and the λ-pseudo-starlike functions as well as the Horadam polynomials. We estimate the second and the third coefficients in the Taylor-Maclaurin expansions of functions belonging to the holomorphic and bi-univalent function class, which we introduce here. Furthermore, we establish the Fekete-Szegö inequality for functions in the family SWΣ(δ,γ,λ,s,t,q,r). Relevant connections of some of the special cases of the main results with those in several earlier works are also pointed out. Our usage here of the basic or quantum (or q-) extension of the familiar Hurwitz-Lerch zeta function Φ(z,s,a) is justified by the fact that several members of this family of zeta functions possess properties with local or non-local symmetries. Our study of the applications of such quantum (or q-) extensions in this paper is also motivated by the symmetric nature of quantum calculus itself.

In a previous Memoirs (Vol. 92, No. 448), Levenberg and Yamaguchi analysed the second variation of the Robin function $-\\lambda(t)$ associated to a smooth variation of domains in $\\mathbb{C}^n$ for $n\\geq 2$. In the current work, the authors study a generalisation of this second variation formula to complex manifolds $M$ equipped with a Hermitian metric $ds^2$ and a smooth, nonnegative function $c$.

In this volume we study noncommutative domains Each such a domain has a universal model Free holomorphic functions, Cauchy transforms, and Poisson transforms on noncommutative domains We associate with each We introduce two numerical invariants, the curvature and We present a commutant lifting theorem for pure In the particular case when

Take three integers m≥0,k≥1, and n≥2. Let a(≢0) be a holomorphic function in a domain D of C such that multiplicities of zeros of a are at most m and divisible by n+1. In this paper, we mainly obtain the following normality criterion: Let F be the family of meromorphic functions on D such that multiplicities of zeros of each f∈F are at least k+m and such that multiplicities of poles of f are at least m+1. If each pair (f,g) of F satisfies that fnf(k) and gng(k) share a (ignoring multiplicity), then F is normal.

This is the first of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 734.Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union.The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in functional analysis, operator theory, several complex variables, topological dynamics, and algebraic, convex, and integral geometry.

We prove that the open unit ball 𝔹 n of 𝕔 n (n ≥ 2) admits a nonsingular holomorphic foliation ℱ by closed complex hypersurfaces such that both the union of the complete leaves of ℱ and the union of the incomplete leaves of ℱ are dense subsets of 𝔹 n . In particular, every leaf of ℱ is both a limit of complete leaves of ℱ and a limit of incomplete leaves of ℱ. This gives the first example of a holomorphic foliation of 𝔹 n by connected closed complex hypersurfaces having a complete leaf that is a limit of incomplete ones. We obtain an analogous result for foliations by complex submanifolds of arbitrary pure codimension q with 1 ≤ q < n.