The multidimensional Hadamard composition and Szeg� kernel

1984 ◽  
Vol 24 (3) ◽  
pp. 317-323
Author(s):  
L. A. Aizenberg ◽  
E. K. Leinartas
Keyword(s):  
Hadamard Composition

Multidimensional Hadamard composition and sums with linear constraints on the summation indices

1989 ◽  
Vol 30 (2) ◽  
pp. 250-255 ◽  
Author(s):  
E. K. Leinartas
Keyword(s):  
Linear Constraints ◽  
Hadamard Composition

Hadamard compositions of Gelfond-Leont'ev derivatives of analytic functions

2020 ◽  
Vol 17 (2) ◽  
pp. 234-255
Author(s):  
Myroslav Sheremeta ◽  
Oksana Mulyava
Keyword(s):  
Analytic Functions ◽  
Derivatives Of ◽  
Hadamard Composition

For analytic functions f and g, the growth of the Hadamard composition of their Gelfond-Leont'ev derivatives is investigated in terms of generalized orders. A relation between the behaviors of the maximal terms of the Hadamard composition of Gelfond-Leont'ev derivatives and those of the Gelfond-Leont'ev derivative of a Hadamard composition is established.

Singular points of the Hadamard composition

1990 ◽  
Vol 42 (12) ◽  
pp. 1545-1547 ◽  
Author(s):  
Yu. F. Korobeinik ◽  
N. N. Mavrodi
Keyword(s):  
Singular Points ◽  
Hadamard Composition

ON HADAMARD COMPOSITION WITH ALGEBRAIC-LOGARITHMIC SINGULARITIES

1958 ◽  
Vol 9 (1) ◽  
pp. 68-72
Author(s):  
R. WILSON
Keyword(s):  
Logarithmic Singularities ◽  
Hadamard Composition

Multidimensional Hadamard composition

1994 ◽  
Vol 35 (5) ◽  
pp. 936-940 ◽  
Author(s):  
M. M. Elin
Keyword(s):  
Hadamard Composition

On Hadamard Composition with a Class of Isolated Singularities

1964 ◽  
Vol s1-39 (1) ◽  
pp. 713-719
Author(s):  
R. Wilson
Keyword(s):  
Isolated Singularities ◽  
Hadamard Composition

scholarly journals Hadamard compositions of Gelfond-Leont’ev-Sǎlǎgean and Gelfond-Leont’ev-Ruscheweyh derivatives of functions analytic in the unit disk

2020 ◽  
Vol 54 (2) ◽  
pp. 115-134
Author(s):  
M.M. Sheremeta
Keyword(s):  
Unit Disk ◽  
Lower Order ◽  
Analytic Functions ◽  
Maximal Term ◽  
Derivatives Of ◽  
Hadamard Composition

For analytic functions $$f(z)=z+\sum\limits_{k=2}^{\infty}f_kz^k \mbox{ and } g(z)=z+\sum\limits_{k=2}^{\infty}g_kz^k$$ in the unit disk properties of the Hadamard compositions $D^n_{l,[S]}f*D^n_{l,[S]}g$ and $D^n_{l,[R]}f*D^n_{l,[R]}g$ of their Gelfond-Leont'ev-S$\check{\text{a}}$l$\check{\text{a}}$gean derivatives $$D^n_{l,[S]}f(z)=z+\sum\limits_{k=2}^{\infty}\left(\frac{l_1l_{k-1}}{l_k}\right)^nf_kz^k$$ and Gelfond-Leont'ev-Ruscheweyh derivatives$$D^n_{l,[R]}f(z)=z+\sum\limits_{k=2}^{\infty}\frac{l_{k-1}l_n}{l_{n+k-1}}f_kz^k$$ are investigated. For study, generalized orders are used. A connection between the growth of the maximal term of the Hadamard composition of Gelfond-Leont'ev-S$\check{\text{a}}$l$\check{\text{a}}$gean derivatives or Gelfond-Leont'ev-Rusche\-weyh derivatives and the growth of the maximal term of these derivatives of Hadamard composition is established. Similar results are obtained in terms of the classical order and the lower order of the growth.

scholarly journals The Hadamard compositions of Dirichlet series absolutely converging in half-plane

2020 ◽  
Vol 53 (1) ◽  
pp. 13-28
Author(s):  
M.M. Sheremeta ◽  
O.M. Mulyava
Keyword(s):  
Dirichlet Series ◽  
Half Plane ◽  
Absolute Convergence ◽  
Hadamard Composition

For Dirichlet series with different finite abscissas of absolute convergence in terms of generalized orders the growth of the Hadamard composition of their derivatives is investigated.A relation between the behavior of the maximal terms of Hadamard composition of derivatives and of the derivative of Hadamard composition is established.

scholarly journals On Hadamard composition of Gelfond-Leont'ev derivatives of entire and analytic functions in the unit disk

2021 ◽  
Vol 13 (1) ◽  
pp. 98-109
Author(s):  
O.M. Mulyava ◽  
M.M. Sheremeta
Keyword(s):  
Entire Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Derivatives Of ◽  
Hadamard Composition

For an entire function and an analytic in the unit disk function the growth of the Hadamard composition of their Gelfond-Leont'ev derivatives is investigated in terms of generalized orders. A relationship between the behaviors of the maximal terms of Hadamard composition of Gelfond-Leont'ev derivatives and of the Gelfond-Leont'ev derivative of Hadamard composition is established.

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