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卷 89, 编号 6 (2025)
Articles
Stability of approximation in classical problems of geometric approximation theory
摘要
Approximative compactness type properties in various problems of $\min$ - and $\max$ -approximation are studied.
This leads naturally to “special points” of approximation theory — these being the spaces characterizable in approximative compactness terms for various classical problems of approximation. These “special points” are CLUR–spaces, Day–Oshman spaces, Anderson–Megginson spaces, CMLUR-spaces, and AT-spaces.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2025;89(6):3-27
3-27
Weak quasiclassical asymptotics of polynomial solutions of three-term recurrence relations of high order
摘要
For polynomials $Q_{n}(z):=z^n + \cdots$ defined by three-term recurrence relations
$Q_{n+1}=zQ_n-a_{n-p+1}Q_{n-p}$ ,
$p\ge {1}$ , of order $p+1$ with the coefficient $a_{n}\equiv a_{n,N}$ (the variable recurrence coefficient) depending on the parameter $N$ ,
the weak asymptotics of $Q_n (z)$ are investigated in the quasi-classical regime as $n \to \infty$ ,
$n/N \to t$ , and $a_{n,N} \to a(t)$ .
The case $p=1$ (orthogonal polynomials) was studied earlier. The results obtained (for $p=2$ ) are applied to the problem of eigenvalues distributions of ensembles of normal random matrices.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2025;89(6):28-44
28-44
On the representations of the $C^*$ -algebra of singular integral operators on a complex contour with discontinuous semi-almost periodic coefficients
摘要
A $C^*$ -algebra generated by one-dimensional singular integral operators on an unbounded complex contour is studied. The coefficients are allowed to have jump
discontinuities at the contour points and stabilize to almost periodic functions
on each arc extending to infinity. All primitive ideals of this algebra are
listed.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2025;89(6):45-84
45-84
Abstract fractional difference inclusions
摘要
In this paper, we consider various classes of the abstract fractional difference inclusions with Weyl fractional derivatives and Riemann–Liouville fractional derivatives. We also provide some new results about the well-posedness of abstract integer-order difference inclusions with Euler forward operators, paying a special attention to the analysis of the existence and uniqueness of
almost periodic and almost automorphic type solutions to abstract fractional difference inclusions.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2025;89(6):85-104
85-104
Segal–Bargmann transform for generalized partial-slice monogenic functions
摘要
The concept of generalized partial-slice monogenic functions has been recently introduced to include the two theories of monogenic functions and of slice monogenic functions over Clifford algebras. The main purpose of this article is to develop the Segal–Bargmann transform and give a Schrödinger representation in the setting of generalized partial-slice monogenic functions. To this end, the generalized partial-slice Cauchy–Kovalevskaya extension plays a crucial role.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2025;89(6):105-130
105-130
Quantitative uniform exponential acceleration of averages along decaying waves
摘要
In this study, utilizing a specific exponential weighting function, we investigate the uniform exponential convergence of weighted Birkhoff averages along decaying waves and delve into several related variants. A key distinction from traditional scenarios is evident here: despite reduced regularity in observables, our method still maintains exponential convergence. In particular, we develop new techniques that yield very precise rates of exponential convergence, as evidenced by numerical simulations. Furthermore, this innovative approach extends to quantitative analyses involving different weighting functions employed by others, surpassing the limitations inherent in prior research. It also enhances the exponential convergence rates of weighted Birkhoff averages along quasi-periodic orbits via analytic observables. To the best of our knowledge, this is the first result on the uniform exponential acceleration beyond averages along quasi-periodic or almost periodic orbits, particularly from a quantitative perspective.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2025;89(6):131-161
131-161
Explicit estimate of the convergence rate in the Riemann localization principle
摘要
The convergence rate in the Riemann localization principle for trigonometric series is estimated.
S. A. Telyakovskii's result for integrable functions is refined.
Functions with $\operatorname{Lip}\alpha$ integral modulus of continuity and functions of bounded variation
are considered.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2025;89(6):162-182
162-182
The second moment of Maass form symmetric square $L$ -functions at the central point
摘要
Recently R. Khan and M. Young proved an order-sharp Lindelöf estimate on the second moment of central values of Maass form symmetric-square $L$ -function
on the interval $T<|t_j|, where $t_j$ is a spectral parameter of the Maass form. We provide another proof of this result.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2025;89(6):183-205
183-205
Single fault detection test sets with respect to stuck-at faults at the outputs of gates in formulas over one basis of Zhegalkin type
摘要
The article establishes the exact values of the Shannon function of the cardinality of a single fault detection test set with respect to stuck-at faults at outputs of gates in formulas over the basis \( \{\, x \& y,\; x \oplus y,\; x \sim y \,\}\ \)
.
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2025;89(6):206-218
206-218
Letter to the editors
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya. 2025;89(6):219-220
219-220