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1.
In this paper, we consider the behavior of rectangular partial sums of the Fourier series of continuous functions of several variables with respect to the trigonometric system. The Fourier series is called -convergent if the limit of rectangular partial sums over all indices
for which
for all j and k exists. In the space of arbitrary even dimension 2m we construct an example of a continuous function with an estimate of the modulus of continuity
such that its Fourier series is -divergent everywhere for any
. 相似文献
2.
A. G. Areshkina 《Mathematical Notes》1998,64(2):154-158
On a measurable space (T, , ) we choose an additive measure: Z (Z is a Banach space) with the following property: for alle , we have
; this measure defines an indefinite integral over the measure onL
2
(T, ,). We prove that if {
n
(t)}
n
=1/
is an orthonormal basis inL
2 and
n
(e)=e
n
(t) d, then any additive measure: Z whose Radon-Nikodým derivatived/d belongs toL
2 is uniquely expandable in a series(e)=
n
=1/
n
n(e) that converges to(e) uniformly with respect toe can be differentiated term-by-term, and satisfies
n
=1/
n
/2
<. In the caseL
2[0,2],Z=, the Fourier series of a 2-periodic absolutely continuous functionF(t) such thatF'(t) L
2[0, 2] is superuniformly convergent toF(t).Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 180–184, August, 1998. 相似文献
3.
Let A be a ring, be an injective endomorphism of A, and let
be the right skew polynomial ring. If all right annihilator ideals of A are ideals, then R is a right Bezout ring
is a right Rickartian right Bezout ring, (e)=e for every central idempotent eA, and the element (a) is invertible in A for every regular aA. If A is strongly regular and n 2, then R/x
n
R is a right Bezout ring
R/x
n
R is a right distributive ring
R/x
n
R is a right invariant ring
(e)=e for every central idempotent eA. The ring R/x
2
R is right distributive
R/x
n
R is right distributive for every positive integer n
A is right or left Rickartian and right distributive, (e)=e for every central idempotent eA and the (a) is invertible in A for every regular aA. If A is a ring which is a finitely generated module over its center, then A[x] is a right Bezout ring
A[x]/x
2
A[x] is a right Bezout ring
A is a regular ring. 相似文献
4.
An operator
mapping a separable reflexive Banach space X into the dual space X is called increasing if
as
. Necessary and sufficient conditions for the superposition operators to be increasing are obtained. The relationship between the increasing and coercive properties of monotone partial differential operators is studied. Additional conditions are imposed that imply the existence of a solution for the equation
with an increasing operator A. 相似文献
5.
The main result is the following theorem. Let
be a commutative Banach algebra with radical R, where the factor algebra
is isomorphic to the algebra of all continuous functions on a totally disconnected compact space. If rn1 /n 0 as n uniformly for r R, rl, then the algebra
is strongly decomposable, i.e., there exists a closed subalgebra B
isomorphic to
such that
=BR.This is a strengthening of the theorem of A. Ya. Khelemskii, who assumed
. There are 4 references.Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 589–592, December, 1967. 相似文献
6.
G. G. Braichev 《Mathematical Notes》1976,19(2):135-140
In this paper it is shown that under conditions of applicability of the operator
to the class [,] =(I,s), 2 1, 2), 1, 2< the equation
y=f has a particular solution of this class vf[, ]. The general form of a solution of the homogeneous equation
y=0 is established. The growth of a solution is investigated by means of a system of conjugate orders and a system of conjugate types. A solvability result is also obtained in the class
, where T is a certain set in R
+
2
depending on the operator
.Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 225–236, February, 1976.In conclusion, the author would like to express his thanks to his adviser, Yu. F. Korobeinik. 相似文献
7.
We prove that if a group G is residually
, then for every
-subgroup of the group G, the set of -roots from this subgroup is a -separable
-subgroup. 相似文献
8.
In this paper, we generalize Bernstein's theorem characterizing the space
by means of local approximations. The closed interval
is partitioned into disjoint half-intervals on which best approximation polynomials of degree
divided by the lengths of these half-intervals taken to the power
are considered. The existence of the limits of these ratios as the lengths of the half-intervals tend to zero is a criterion for the existence of the
th derivative of a function. We prove the theorem in a stronger form and extend it to the spaces
. 相似文献
9.
D. V. Millionshchikov 《Mathematical Notes》2005,77(1-2):61-71
The cohomology H* (G/,) of the de Rham complex *(G/) of a compact solvmanifold G/ with deformed differential d = d + , where is a closed 1 -form, is studied. Such cohomologies naturally arise in Morse-Novikov theory. It is shown that, for any completely solvable Lie group G containing a cocompact lattice G, the cohomology H*(G/, ) is isomorphic to the cohomology H*(
) of the tangent Lie algebra
of the group G with coefficients in the one-dimensional representation :
defined by () = (). Moreover, the cohomology H
*(G/,) is nontrivial if and only if -[] belongs to a finite subset
of H
1(G/,) defined in terms of the Lie algebra
.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 67–79.Original Russian Text Copyright © 2005 by D. V. Millionshchikov.This revised version was published online in April 2005 with a corrected issue number. 相似文献
10.
Suppose that
is an arbitrary finite complex Borel measure on the interval
is its Poisson integral,
and
are the conjugate harmonics of
, and
is the nontangential limiting value of the analytic function
as
. In this paper, we consider the problem of representing the analytic function
in terms of its boundary values
. 相似文献
11.
R. A. Doney 《Probability Theory and Related Fields》1989,81(2):239-246
Summary Let
x
denote the time at which a random walk with finite positive mean first passes into (x, ), wherex0. This paper establishes the asymptotic behaviour of Pr {
x
>n} asn for fixedx in two cases. In the first case the left hand tail of the step-distribution is regularly varying, and in the second the step-distribution satisfies a one-sided Cramér type condition. As a corollary, it follows that in the first case
Pr {
x
>n}/Pr{
0
>n} coincides with the limit of the same quantity for recurrent random walk satisfying Spitzer's condition, but in the second case the limit is more complicated. 相似文献
12.
Yuanji Cheng 《Czechoslovak Mathematical Journal》1997,47(4):681-687
In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems
where –p is the p-Laplace operator, p > 1 and is a C
1,-domain in
. We prove an analogue of [7, 16] for the eigenvalue problem with
and obtain a non-existence result of positive solutions for the general systems. 相似文献
13.
In this paper, we suggest a new functional approach to the study of group classes which enables us to describe all formations and Fitting classes of finite groups in the language of functions. The notions of
-fibered formation and of
-fibered Fitting class with direction are introduced. A direction is defined as a mapping of the set
of all primes into the set of all nonempty Fitting formations. The existence of infinitely many mappings of this kind makes it possible to construct new forms of formations and Fitting classes for a given nonempty set
. In particular, an
-local formation is an
-fibered formation with a direction such that
for any prime p. In the paper we study some basic properties of
-fibered formations and of
-fibered Fitting classes with direction and obtain the structure of their minimal satellites for a given . 相似文献
14.
V. M. Badkov 《Mathematical Notes》1973,13(5):453-459
For the polynomials {pn(t)}
0
, orthonormalized on [–1, 1] with weightp(t) = (1–t) (1+t)
v=1
m
, we obtain necessary and sufficient conditions for boundedness of the sequences of norms: 1)
2)
and 3)
with the conditions that
on [–1, 1] and (H,)–1 L2(0, 2), where(H,) is the modulus of continuity in C(–1, 1) of function H.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 759–770, May, 1973. 相似文献
15.
Let U
j be a finite system of functionals of the form
, and let
be the subspace of the Sobolev space
, 1 p +, that consists only of functions g such that U
j(g) = 0 for k
j < r. It is assumed that there exists at least one jump
j
for every function
j
, and if
j
=
s
for j s, then k
j k
s. For the K-functional
we establish the inequality
, where the constant c > 0 does not depend on (0; 1], the functions f belong to L
p, and r = 1, ¨, n. On the basis of this inequality, we also obtain estimates for the K-functional in terms of the modulus of smoothness of a function f. 相似文献
16.
R. Vosylius 《Lithuanian Mathematical Journal》2003,43(2):210-220
In the canonical smooth fiber bundles : n+1 n endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups
and construct
-invariant generalizations of differentiable connections. In both regular and special cases of the representations of the relevant groups
, we found all the affine nonholonomic 1-, 2-, and 1, 2-connections of the first order (see [4]) possessing the local Lie groups of transformations
and also described the respective
-invariant planar connections. 相似文献
17.
For any probability on the space of d×d stochastic matrices we associate a probability
; on a finite group—a subgroup of the permutation group—related to the kernel of the semigroup generated by the support of . We show that n converges iff
n converges. 相似文献
18.
I. V. Protasov 《Ukrainian Mathematical Journal》1995,47(4):588-593
We construct two new series of closed left ideals of the semigroup
of ultrafilters of a topological group (G, ). The first series gives a disjunctive decomposition of -absorbing ultrafilters. Under certain restrictions on the topology of the group (G, ), the second series gives a disjunctive decomposition of the semigroup of free ultrafilters. For a nondiscrete metrizable topological group (G, ), we construct a large free subsemigroup of the semigroup
.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 506–511, April, 1995. 相似文献
19.
A sufficient condition for the stability of completeness of systems of exponentials
with exponent shifts
n in spaces of functions continuous onb and holomorphic inside a compact convex set with nonempty interior is obtained. This condition is a generalization of an important special case of the corresponding result for the closed interval due to Redheffer and Alexander. 相似文献
20.
Stefano Cavallaro 《Algebras and Representation Theory》2000,3(2):175-186
Let
be an Abelian unital C
*-algebra and let
denote its Gelfand spectrum. We give some necessary and sufficient conditions for a nondegenerate representation of
to be unitarily equivalent to a representation in which the elements of
act multiplicatively, by their Gelfand transforms, on a space L
2(
,), where is a positive measure on the Baire sets of
. We also compare these conditions with the multiplicity-free property of a representation. 相似文献