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1

Slice holomorphic solutions of some directional differential equations with bounded L-index in the same direction

Bandura Andriy, Skaskiv Oleh, Smolovyk Liana

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

482--489

EN

In the paper we investigate slice holomorphic functions F : Cn→C having bounded L-index in a direction, i.e. these functions are entire on every slice {z0 +tb : t∈C} for an arbitrary z0∈Cn and for the fixed direction b∈Cn \ {0}, and (∃m0∈Z+) (∀m∈Z+) (∀z∈Cn) the following inequality holds [wzór], where L : Cn→R+ is a positive continuous function, [wzór] for p≥2. Also, we consider index boundedness in the direction of slice holomorphic solutions of some partial differentia equations with partial derivatives in the same direction. There are established sufficient conditions providing the boundedness of L-index in the same direction for every slie holomorphic solutions of these equations.

2

Defective functions of meromorphic functions in the unit disc

Ciechanowicz E.

Journal of Applied Analysis

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2016

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Vol. 22, nr 1

15--26

EN

Let f be a meromorphic function in the unit disc and (aν)kν=1 a set of distinct meromorphic functions small with respect to f. An analogue of the second main theorem for f and (aν)kν=1 is given. Upper limits for the sum of defects of an admissible meromorphic function and an admissible holomorphic function follow. For meromorphic and holomorphic functions in the unit disc and their small functions the analogues of Ullrich's theorem are presented.

3

On certain functions with positive real part

Sendrutiu R.

Journal of Mathematics and Applications

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2010

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Vol. 32

85-90

4

Elements of D'Lq (R) as boundary values of holomorphic functions

Skórnik U.

Demonstratio Mathematica

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2000

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Vol. 33, nr 3

657-663

EN

In this paper we give a boundary value characterization of the space D'Lp(R) (see also [4]). Namely, we will show that every distribution that belongs to the space D'Lp(R) can be represented by analytic functions. We will also show that analytic functions fulfilling certain growth conditions have their boundary values in the space D'Lp (R). The characterization of holomorphic function spaces whose elements have boundary values in spaces of distributions and ultradistributions has a long history, see [2]-[6], [8] and [9].

5

On a Sufficirnt Condition for the Inivalency of Functions

Fuka J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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1999

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Vol. 6

21--22

6

On the Łojasiewicz exponent of the gradient of holomorphic functions

Bogusławska M.

Bulletin of the Polish Academy of Sciences. Mathematics

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1999

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Vol. 47, no 4

337-343

EN

We show that the Łojasiewicz exponent L[sub o] (grad f) at zero of the gradient of a distinguished pseudo-polynomial f [...] is attained on the zero-set of f'[sub y].

7

On factorization of polynomials with holomorphic coefficients

Frontczak M., Skibiński A., Spodzieja S.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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Vol. 46, no 1

39-54

EN

In the paper some equivalent conditions to pointwise reducibility of polynomials with holomorphic coefficients (in an arbitrary connected set) are given.