Mathematical Notes

Items from 1 to 20 out of 2,757 results

article

Concerning the multiplicators of Fourier series in the trigonometric system

E. D. Nursultanov

Mathematical Notes > 1998 > 63 > 2 > 205-214

In this paper we prove theorems on multiplicators of Fourier series inL _p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed.

article

Functions of two variables continuous along straight lines

E. E. Shnol'

Mathematical Notes > 1998 > 64 > 1 > 136-136

article

Regularized traces of nonself-adjoint operators

V. V. Dubrovskii

Mathematical Notes > 1999 > 65 > 5 > 658-662

article

Concerning the multiplicators of fourier series in the trigonometric system

E. D. Nursultanov

Mathematical Notes > 1999 > 65 > 6 > 801-801

The online version of the original article can be found at http://dx.doi.org/10.1007/BF02308760

article

Regularized traces of non-self-adjoint operators

V. V. Dubrovskii

Mathematical Notes > 2000 > 67 > 2 > 266-266

article

Properties of the Absolute That Affect Smoothness of Flows on Closed Surfaces

S. Kh. Aranson, E. V. Zhuzhoma

Mathematical Notes > 2000 > 68 > 5-6 > 695-703

Let $$M_g^2$$ be a closed orientable surface of genus $$g \geqslant 2$$ , endowed with the structure of a Riemann manifold of constant negative curvature. For the universal covering $$\Delta$$ , there is the notion of absolute, each of whose points determines an asymptotic direction of a bundle of parallel equidirected geodesics. In the paper it is proved that there is a set $$U_g$$...

article

Q-Transformations and Q-Equivalence

S. G. Ivanov

Mathematical Notes > 2000 > 68 > 5-6 > 661-663

article

Strong Positivity in Right-Invariant Order on Braid Groups and Quasipositivity

S. Yu. Orevkov

Mathematical Notes > 2000 > 68 > 5-6 > 588-593

Dehornoy constructed a right invariant order on the braid group B _n uniquely defined by the condition $$\beta _0 \sigma _i \beta _1 >1{\text{ if }}\beta _0 ,\beta _1$$ are words in $$\sigma _{i + 1}^{ \pm 1} ,...,\sigma _{n - 1}^{ \pm 1}$$ . A braid is called strongly positive if $$\alpha \beta \alpha ^{ - 1} >1$$ for any $$\alpha \in B_n$$ . In the present paper it is...

article

A New Representation of the Hamiltonian Operator for Bosons and Fermions. Quantization of Free Energy and Dependence of the Landau Criterion on Temperature

V. P. Maslov

Mathematical Notes > 2000 > 68 > 5-6 > 800-802

article

On the Difference between the Number of Prime Divisors from Subsets for Consecutive Integers

N. M. Timofeev, M. B. Khripunova

Mathematical Notes > 2000 > 68 > 5-6 > 614-626

Suppose that E ₁,E ₂ are arbitrary subsets of the set of primes and $$g_{\text{1}} \left( n \right),g_{\text{2}} \left( n \right)$$ are additive functions taking integer values such that $$g_i \left( p \right) = 1{\text{ if }}p \in E<Subscript>i ,{\text{ and }}g_i \left( p \right) = 0$$ otherwise, i=1,2. Set $$E_i (x) = \sum \limits_{p \leqslant x, p \in E_i} \frac{1}{p}, i =...

article

Asymptotics of the Solution to the Cauchy Problem for Linear Parabolic Equations of Second Order with Small Diffusion

V. M. Khametov

Mathematical Notes > 2000 > 68 > 5-6 > 775-789

This paper is devoted to constructing an asymptotics of the solution to the Cauchy problem for a linear parabolic equation of second order with variable coefficients containing a small parameter at the highest derivative. Sufficient conditions for the existence and uniqueness of the “multiplicative” asymptotic expansion of the global solution of the problem are given.

article

A Method of Deducing L-Polyhedra for n-Lattices

E. P. Baranovskii, P. G. Kononenko

Mathematical Notes > 2000 > 68 > 5-6 > 704-712

We suggest a method for selecting an L-simplex in an L-polyhedron of an n-lattice in Euclidean space. By taking into account the specific form of the condition that a simplex in the lattice is an L-simplex and by considering a simplex selected from an L-polyhedron, we present a new method for describing all types of L-polyhedra in lattices of given dimension n. We apply the method to deduce all types...

article

On Rearrangements of the Haar System in L ^p

D. Z. Marshan

Mathematical Notes > 2000 > 68 > 5-6 > 737-739

In this paper we study operators rearranging the Haar system in each bundle. It is proved that the norm of any nonidentical rearrangement admits a nontrivial lower bound in L ^p spaces, $$p \ne {\text{2}}$$ .

article

General Approach to Integrating Invertible Dynamical Systems Defined by Transformations from the Cremona group Cr(P _k ⁿ ) of Birational Transformations

K. V. Rerikh

Mathematical Notes > 2000 > 68 > 5-6 > 594-601

A general approach is developed for integrating an invertible dynamical system defined by the composition of two involutions, i.e., a nonlinear one which is a standard Cremona transformation, and a linear one. By the Noether theorem, the integration of these systems is the foundation for integrating a broad class of Cremona dynamical systems. We obtain a functional equation for invariant homogeneous...

article

On the Spectrum of Degenerate Operator Equations

V. V. Kornienko

Mathematical Notes > 2000 > 68 > 5-6 > 576-587

We study the distribution in the complex plane $$\mathbb{C}$$ of the spectrum of the operator $$L = L\left( {\alpha ,a,A} \right),{\text{ }}\alpha \in \mathbb{R},{\text{ }}\alpha \in \mathbb{C}$$ , generated by the closure in $$H = \mathcal{L}_2 \left( {0,b} \right) \otimes \mathfrak{H}$$ of the operation $$t^\alpha aD_t^2 + A$$ originally defined on smooth functions $$u\left(...

article

On Zeros of Functions of Mittag--Leffler Type

A. M. Sedletskii

Mathematical Notes > 2000 > 68 > 5-6 > 602-613

As is well known, the asymptotics of zeros of functions of Mittag--Leffler type $$E_\rho \left( {z;\mu } \right) = \sum\limits_{n = 0}^\infty {\frac{{z^n }}{{\Gamma \left( {\mu + {n \mathord{\left/ {\vphantom {n \rho }} \right. \kern-\nulldelimiterspace} \rho }} \right)}}} ,{\text{ }}\rho >0,{\text{ }}\mu \in \mathbb{C},$$ describes the behavior of zeros outside a disk of sufficiently large...

article

On the Determination of Free Evolution in the Lax--Phillips Scattering Scheme for Second-Order Operator-Differential Equations

S. A. Kuzhel

Mathematical Notes > 2000 > 68 > 5-6 > 724-729

The paper presents some necessary and sufficient conditions on abstract positive self-adjoint operators L under which the operator-differential equation $$u_{tt} = - L_u$$ determines a free evolution in the Lax--Phillips scattering scheme.

article

On Lower Bounds for the L ₁-Norm of Exponential Sums

M. Z. Garaev

Mathematical Notes > 2000 > 68 > 5-6 > 713-720

In the paper a method for finding lower bounds of the L ₁-norm of some exponential sums is described.

article

On the Simultaneous Triangulability of Matrices

Yu. A. Al'pin, N. A. Koreshkov

Mathematical Notes > 2000 > 68 > 5-6 > 552-555

Two necessary and sufficient criteria for the simultaneous triangulability of two complex matrices are established. Both of them admit a finite verification procedure. To prove the first criterion, classical theorems from Lie algebra theory are used, and known sufficient conditions of triangulability are also given a natural interpretation in terms of this theory. The other criterion is discussed...

article

A Probabilistic Approach to the Problem of the Defects of Admissible Sets in a Lattice

A. M. Raigorodskii

Mathematical Notes > 2000 > 68 > 5-6 > 770-774

New estimates for the defect of the admissible set in a lattice are obtained for a sufficiently large class of sequences.

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Mathematical Notes

Concerning the multiplicators of Fourier series in the trigonometric system

Functions of two variables continuous along straight lines

Regularized traces of nonself-adjoint operators

Concerning the multiplicators of fourier series in the trigonometric system

Regularized traces of non-self-adjoint operators

Properties of the Absolute That Affect Smoothness of Flows on Closed Surfaces

Q-Transformations and Q-Equivalence

Strong Positivity in Right-Invariant Order on Braid Groups and Quasipositivity

A New Representation of the Hamiltonian Operator for Bosons and Fermions. Quantization of Free Energy and Dependence of the Landau Criterion on Temperature

On the Difference between the Number of Prime Divisors from Subsets for Consecutive Integers

Asymptotics of the Solution to the Cauchy Problem for Linear Parabolic Equations of Second Order with Small Diffusion

A Method of Deducing L-Polyhedra for n-Lattices

On Rearrangements of the Haar System in L ^p

General Approach to Integrating Invertible Dynamical Systems Defined by Transformations from the Cremona group Cr(P _k ⁿ ) of Birational Transformations

On the Spectrum of Degenerate Operator Equations

On Zeros of Functions of Mittag--Leffler Type

On the Determination of Free Evolution in the Lax--Phillips Scattering Scheme for Second-Order Operator-Differential Equations

On Lower Bounds for the L ₁-Norm of Exponential Sums

On the Simultaneous Triangulability of Matrices

A Probabilistic Approach to the Problem of the Defects of Admissible Sets in a Lattice

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