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A note on one of the Bernstein theorems

Jiří Brabec (1993)

Mathematica Bohemica

One of the Bernstein theorems that the class of bounded functions of the exponential type is dense in the space of bounded and uniformly continuous functions. This theorem follows from a convergence theorem for some interpolating operators on the real axis.

A note on regularly asymptotic points

Jiří Jelínek (1996)

Commentationes Mathematicae Universitatis Carolinae

A condition of Schmets and Valdivia for a boundary point of a domain in the complex plane to be regularly asymptotic is ameliorated.

A note on some results of Li and Li

Sujoy Majumder, Somnath Saha (2018)

Mathematica Bohemica

The purpose of the paper is to study the uniqueness problems of linear differential polynomials of entire functions sharing a small function and obtain some results which improve and generalize the related results due to J. T. Li and P. Li (2015). Basically we pay our attention to the condition λ ( f ) 1 in Theorems 1.3, 1.4 from J. T. Li and P. Li (2015). Some examples have been exhibited to show that conditions used in the paper are sharp.

A Note on the Alexander Theorem on the Complex Plane

Sylwester Zając (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

We investigate the Banach manifold consisting of complex r functions on the unit disc having boundary values in a given one-dimensional submanifold of the plane. We show that ∂/∂λ̅ restricted to that submanifold is a Fredholm mapping. Moreover, for any such function we obtain a relation between its homotopy class and the Fredholm index.

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