Geodesic
Existence Theorems for Momentum Representations Generalized in the Sense of Dzyadyk
Matematičeskie zametki, Tome 75 (2004) no. 2, pp. 253-260.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, in particular, we prove that, for any sequence of complex numbers $\{c_n\}_{n=0}^\infty$, there exists a closed linear operator $A$ acting in the Hilbert space and two vectors $x$ and $y$ lying in the domains of definition of all powers of the operator $A$ for which the relation $c_n=(A^n x, y)$ holds. But if the series $\sum_{n=0}^\infty c_n z^n$ has radius of convergence $R > 0$, then in the representation $c_n=(A^nx,y)$, the operator $A$ can be chosen to be bounded with a spectral radius equal to $1/R$. 
@article{MZM_2004_75_2_a7,
     author = {G. V. Radzievskii},
     title = {Existence {Theorems} for {Momentum} {Representations} {Generalized} in the {Sense} of {Dzyadyk}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {253--260},
     publisher = {mathdoc},
     volume = {75},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a7/}
}
TY  - JOUR
AU  - G. V. Radzievskii
TI  - Existence Theorems for Momentum Representations Generalized in the Sense of Dzyadyk
JO  - Matematičeskie zametki
PY  - 2004
SP  - 253
EP  - 260
VL  - 75
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a7/
LA  - ru
ID  - MZM_2004_75_2_a7
ER  - 
%0 Journal Article
%A G. V. Radzievskii
%T Existence Theorems for Momentum Representations Generalized in the Sense of Dzyadyk
%J Matematičeskie zametki
%D 2004
%P 253-260
%V 75
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a7/
%G ru
%F MZM_2004_75_2_a7
G. V. Radzievskii. Existence Theorems for Momentum Representations Generalized in the Sense of Dzyadyk. Matematičeskie zametki, Tome 75 (2004) no. 2, pp. 253-260. http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a7/

[1] Dzyadyk V. K., “Ob obobschenii problemy momentov”, Dokl. AN UkrSSR. Ser. A, fiz.-matem. i tekhn. nauk., 1981, no. 6, 8–12 | MR | Zbl

[2] Dzyadyk V. K., Approksimatsionnye metody resheniya differentsialnykh i integralnykh uravnenii, Naukova dumka, Kiev, 1988 | MR

[3] Dzyadyk V. K., Golub A. P., Obobschennaya problema momentov i approksimatsii Pade, Preprint 81.58, AN UkrSSR, In-t matematiki, Kiev, 1981 | MR

[4] Golub A. P., Obobschennye momentnye predstavleniya i ratsionalnye approksimatsii, Preprint 87.25, AN UkrSSR, In-t matematiki, Kiev, 1987 | MR

[5] Beiker Dzh., Greivs-Morris P., Approksimatsii Pade, Mir, M., 1986 | MR

[6] Gofman K., Banakhovy prostranstva analiticheskikh funktsii, IL, M., 1963

[7] Bart H., Gohberg I., Kaashoek M. A., Minimal Factorization of Matrix and Operator Functions. Operator Theory: Advances and Applications, 1, Birkhäuser, Basel–Boston, 1979 | MR | Zbl

[8] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl