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Vol 88, No 1 (2024)
Articles
On unconditionality of fractional Rademacher chaos in symmetric spaces
Abstract
We study density estimates of an index set $\mathcal{A}$under which the unconditionality (or even the weaker property of randomunconditional divergence) of the corresponding Rademacher fractional chaos $\{r_{j_1}(t) \cdot r_{j_2}(t) \cdots r_{j_d}(t)\}_{(j_1,j_2,…,j_d)\in \mathcal{A}}$ in a symmetric space $X$ implies its equivalence in $X$to the canonical basis in $\ell_2$. In the special case of Orlicz spaces $L_M$, unconditionality of this system is also shown to be equivalent to the fact thata certain exponential Orlicz space embeds into $L_M$.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2024;88(1):3-20
3-20
Kolmogorov widths of an intersection of a finite family of Sobolev classes
Abstract
Order estimates for the Kolmogorov widths of an intersection of Sobolev classeson a $d$-dimensional John domain and on the 1-dimensional torus are obtained.In particular, one Galeev's result is generalized.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2024;88(1):21-46
21-46
Ground states for fractional Choquard equations with doubly critical exponents and magnetic fields
Abstract
In this paper, we investigate the ground states for the fractional Choquard equations with doubly critical exponents and magnetic fields. We prove that the equation has a ground state solution by using the Nehari method and the Pokhozhaev identity.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2024;88(1):47-57
47-57
On weak solvability of fractional models of viscoelastic high order fluid
Abstract
In this paper, we establish the existence of a weak solution to theinitial boundary value problem for the motion equations ofviscoelastic incompressible fluid with constitutive lawcontaining high-order fractional derivatives and with memoryalong the trajectories of the velocity field. The proof is by approximation of the original problem by a sequence ofregularized problems followed by a passage to the limit based onappropriate a priori estimates. Methods of the theory of fractionalderivatives calculus and the theory of regular Lagrangian flows(generalization of the classical solution of ODE systems) are used.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2024;88(1):58-81
58-81
On quadratic subfields of generalized quaternion extensions
Abstract
We give necessary and sufficient conditions for the embeddingof a quadratic extension of a number field $k$ into an extensionwith group of generalized quaternions; in this case, the caseof both a cyclic kernel and a generalized quaternion is considered.As a consequence, it is proved that the class of ultrasolvable$2$-extensions with cyclic kernel does not coincide with the classof non-semidirect extensions. Sufficient conditions are also givenfor the embedding of quadratic extensions $k(\sqrt{d_1})/k$,$k(\sqrt{d_2})/k$, $k(\sqrt{d_1d_2})/k$ of a number field $k$into a generalized quaternion extension $L/k$. Related examples are given.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2024;88(1):82-97
82-97
On the construction of families of optimal recovery methods for linear operators
Abstract
The paper proposes an approach for construction of families of optimal methodsfor the recovery of linear operators from inaccurately given information.The proposed method of construction is then applied to recover derivatives from inaccurately specified otherderivatives in the multidimensional case and to recover solutions of the heat equationfrom inaccurately specified temperature distributions at some time instants.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2024;88(1):98-120
98-120
Interpolating asymptotic integration methodsfor second-order differential equations
Abstract
The problem of asymptotic behaviour at infinity of solutionsto second-order differential equation can be reduced via the Liouville transformto that ofan equation with almost constant coefficients. In the present paper,we compare various methods of asymptotic integration in application tothe reduced equation $u"-(\lambda^2+\varphi(t))u=0$ and interpolatethe corresponding results in the case $\operatorname{Re}\lambda>0$,provided that a complex-valued function $\varphi(t)$ is in a certain sense smallfor large values of the argument.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2024;88(1):121-140
121-140
Distributions of zeros and masses of entire andsubharmonic functions with restrictions on their growth along the strip
Abstract
Let $\mathrm Z$ and $\mathrm W$ be distributions of points on the complexplane $\mathbb C$. The following problem dates back toF. Carlson, T. Carleman, L. Schwartz, A. F. Leont'ev, B. Ya. Levin,J.-P. Kahane, and others. For which $\mathrm Z$ and $\mathrm W$,for an entire function $g\neq 0$ of exponential type which vanishes on $\mathrm W$, thereexists an entire function $f\neq 0$ of exponential typethat vanishes on $\mathrm Z$ and is such that $|f|\leqslant |g|$ on the imaginary axis?The classical Malliavin–Rubel theorem of the early 1960s completelysolves this problem for “positive” $\mathrm Z$ and $\mathrm W$ (which lie onlyon the positive semiaxis). Several generalizations of this criterion wereestablished by the author of the present paper in the late 1980s for “complex”$\mathrm Z \subset \mathbb C$ and $\mathrm W\subset \mathbb C$ separatedby angles from the imaginary axis, with some advances in the 2020s.In this paper, we solve more involved problems in a more general subharmonicframework for distributions of masses on $\mathbb C$. All the previouslymentioned results can be obtained from the main results of this paperin a much stronger form (even for the initial formulation for distributionsof points $\mathrm Z$ and $\mathrm W$ and entire functions $f$ and $g$ of exponential type).Some results of the present paper are closely relatedto the famous Beurling–Malliavin theorems on the radius of completeness and a multiplier.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2024;88(1):141-202
141-202