2018
Том 70
№ 9

All Issues

Kochubei A. N.

Articles: 13
Article (English)

Linear and nonlinear heat equations on a $p$ -adic ball

Kochubei A. N.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 2. - pp. 193-205

We study the Vladimirov fractional differentiation operator $D^{\alpha}_N,\; \alpha > 0,\; N \in Z$, on a $p$-adic ball B$B_N = \{ x \in Q_p : | x|_p \leq p^N\}$. To its known interpretations via the restriction of a similar operator to $Q_p$ and via a certain stochastic process on $B_N$, we add an interpretation as a pseudodifferential operator in terms of the Pontryagin duality on the additive group of $B_N$. We investigate the Green function of $D^{\alpha}_N$ and a nonlinear equation on $B_N$, an analog of the classical equation of porous medium.

Anniversaries (Ukrainian)

Anatolii Mykhailovych Samoilenko (on his 80th birthday)

Antoniouk A. Vict., Berezansky Yu. M., Boichuk A. A., Gutlyanskii V. Ya., Khruslov E. Ya., Kochubei A. N., Korolyuk V. S., Kushnir R. M., Lukovsky I. O., Makarov V. L., Marchenko V. O., Nikitin A. G., Parasyuk I. O., Pastur L. A., Perestyuk N. A., Portenko N. I., Ronto M. I., Sharkovsky O. M., Tkachenko V. I., Trofimchuk S. I.

Full text (.pdf)

Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 3-6

Anniversaries (Ukrainian)

Myroslav L’vovych Horbachuk (on his 75 th birthday)

Berezansky Yu. M., Gerasimenko V. I., Khruslov E. Ya., Kochubei A. N., Mikhailets V. A., Nizhnik L. P., Samoilenko A. M., Samoilenko Yu. S.

Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 451-454

Article (Ukrainian)

Myroslav L’vovych Horbachuk (on his 70th birthday)

Adamyan V. M., Berezansky Yu. M., Khruslov E. Ya., Kochubei A. N., Kuzhel' S. A., Marchenko V. O., Mikhailets V. A., Nizhnik L. P., Ptashnik B. I., Rofe-Beketov F. S., Samoilenko A. M., Samoilenko Yu. S.

Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 4. - pp. 439–442

Article (English)

Distributed-order calculus: An operator-theoretic interpretation

Kochubei A. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 4. - pp. 478–486

Within the Bochner-Phillips functional calculus and Hirsch functional calculus, we describe the operators of distributed-order differentiation and integration as functions of the classical operators of differentiation and integration, respectively.

Article (English)

Strongly Nonlinear Differential Equations with Carlitz Derivatives over a Function Field

Kochubei A. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 669–678

In earlier papers the author studied some classes of equations with Carlitz derivatives for $\mathbb{F}_q$ -linear functions, which are the natural function field counterparts of linear ordinary differential equations. Here we consider equations containing self-compositions $u \circ u ... \circ u$ of the unknown function. As an algebraic background, imbeddings of the composition ring of $\mathbb{F}_q$ -linear holomorphic functions into skew fields are considered.

Article (Ukrainian)

The liouville operator

Kochubei A. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 12. - pp. 1664–1671

Article (Ukrainian)

Extension theory for symmetric operators and boundary value problems for differential equations

Gorbachuk M. L., Gorbachuk V. I., Kochubei A. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1299–1313

Article (Ukrainian)

One-dimensional point interactions

Kochubei A. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1391–1395

Article (Ukrainian)

Generalized solutions of operator-differential equations

Kochubei A. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 6. - pp. 703–707

Article (Ukrainian)

Self-adjointness of a differential operator with unbounded singular operator coefficient

Kochubei A. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1976. - 28, № 4. - pp. 453–462

Article (Ukrainian)

On the self-adjointness and on the nature of the spectrum of certain classes of abstract differential operators

Kochubei A. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1973. - 25, № 6. - pp. 811—815

Article (Ukrainian)

On best approximation in normed modules

Kochubei A. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1973. - 25, № 1. - pp. 103—106