2018
Том 70
№ 4

Kochubei A. N.

Articles: 13
Article (English)

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

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)

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

Anniversaries (Ukrainian)

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

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

Article (Ukrainian)

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

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

Article (English)

Distributed-order calculus: An operator-theoretic interpretation

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

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

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

Article (Ukrainian)

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

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

Article (Ukrainian)

One-dimensional point interactions

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

Article (Ukrainian)

Generalized solutions of operator-differential equations

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

Article (Ukrainian)

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

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

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

Article (Ukrainian)

On best approximation in normed modules

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