Related papers: Normal families and linear differential equation

A.A. Suslin proved a normality theorem for an elementary linear group and V.I. Kopeiko extended this result of Suslin for a symplectic group defined with respect to the standard skew-symmetric matrix of even size. We generalized the result…

In this paper, we prove normality criteria for families of meromorphic functions involving sharing of a holomorphic function by a certain class of differential polynomials. Results in this paper extends the works of different authors…

We classify all graphs for which the Rees algebras of their edge ideals are normal and have regularity equal to their matching numbers.

We give a new and simple proof of the fact that a finite family of analytic functions has a zero Wronskian only if it is linearly dependent.

For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.

We prove that if two normed-algebra-valued cosine families indexed by a single Abelian group, of which one is bounded and comprised solely of scalar elements of the underlying algebra, differ in norm by less than $1$ uniformly in the…

We define a random Liouville function (\lambda_Q) which depends on a random set (Q) of primes and prove that (A_Q = \{n \in \mathbb{N} | \lambda_Q(n) = -1 \}) is normal almost everywhere. This fact enables us to generate a family of normal…

We show that the marginal semigroup of a binary graph model is normal if and only if the graph is free of K_4 minors. The technique, based on the interplay of normality and the geometry of the marginal cone, has potential applications to…

We show that a family ${\cal F}$ of meromorphic functions in a domain $D$ satisfying $$\frac{|f^{(k)}|}{1+|f^{(j)}|^\alpha}(z)\ge C \qquad \mbox{for all} z\in D \mbox{and all} f\in {\cal F}$$ (where $k$ and $j$ are integers with $k>j\ge 0$…

It is known that if f is a continuous function on the complex plane which extends holomorphically from each circle surrounding the origin then f is not necessarily holomorphic. In the paper we prove that if, in addition, f extends…

In this paper, we prove some value distribution results which lead to some normality criteria for a family of analytic functions. These results improve some recent results.

We give a simple algorithm that enables us to determine whether a subgroup of finite index of the Hecke group is normal.

It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…

In this paper we prove that complete families of smooth and projective curves, of genusg>2, in characteristic p>0, with a constant geometric fundamental group, are isotrivial.

We prove the existence of Siegel disks with smooth boundaries in most families of holomorphic maps fixing the origin. The method can also yield other types of regularity conditions for the boundary. The family is required to have an…

Let $A$ and $B$ be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.

We improve well-known results concerning normal families and shared values of meromorphic functions in the plane. In particular, we obtain two corollaries concerning meromorphic functions $f \colon {\mathbb C} \to {\widehat{\mathbb C}}$: i)…

A real number is called simply normal to base $b$ if every digit $0,1,\ldots ,b-1$ should appear in its $b$-adic expansion with the same frequency $1/b$. A real number is called normal to base $b$ if it is simply normal to every base $b,…

The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation…

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of…