共查询到20条相似文献，搜索用时 437 毫秒
1.
The paper deals with the problem of recovering the parameters (functions)
and
of the Maxwell dynamical system
(tan is the tangent component;
is a solution) by the response operator
(
is the normal). The parameters determine the velocity
, the c-metric
, and the time
. It is shown that for any fixed
, the operator
determines
and
in
uniquely. Bibliography: 15 titles. 相似文献
2.
In what follows, $C$ is the space of
-periodic continuous functions; P is a seminorm defined on C, shift-invariant, and majorized by the uniform norm;
is the mth modulus of continuity of a function f with step h and calculated with respect to P;
,
(
),
, ,
Theorem 1.
Let
. Then
For some values of
and seminorms related to best approximations by trigonometric polynomials and splines in the uniform and integral metrics, the inequalities are sharp. Bibliography: 6 titles. 相似文献
3.
In what follows, C is the space of
-periodic continuous real-valued functions with uniform norm,
is the first continuity modulus of a function
with step h, H
n is the set of trigonometric polynomials of order at most n,
is the set of linear positive operators
(i.e., of operators such that
for every
),
is the space of square-integrable functions on
, It is proved that
coincides with the smallest eigenvalue of some matrix of order n+1. The main result of the paper states that, for every
does not exceed and, for
, is equal to the minimum of the quadratic functional over the unit sphere of
. Then it is calculated that
Bibliography: 19 titles. 相似文献
4.
Let
be the Hecke eigenbasis of the space
of
-cusp forms of weight 2. Let p be a prime. Let
be the Hecke L-series of form
. The following statements are proved: and We also give a correct proof of a previous author's theorem on automorphic L-functions. Bibliography: 12 titles. 相似文献
5.
We apply a variant of the method of the extremal metric to some problems concerning extremal decompositions and related problems. Let
be a system of distinct points on
and let
be the family of all systems
of nonoverlapping simply connected domains on
such that
. Let where
is the reduced module of the domain
with respect to the point
. At present, the problem concerning the value
was solved completely for
. In this work, we continue the previous author's investigations and consider the case
. In addition, we consider the problem concerning the maximum of the sum in the family
introduced above, where
, are arbitrary points of the circle
, and is a positive number. We prove that if
, then the maximum is attained only for systems of equidistant points of the circle
. For
, this result was obtained earlier by Dubinin who applied the method of symmetrization. It is shown that if
, where
is an even number, then equidistant points of the circle
do not realize the indicated maximum. Bibliography: 11 titles. 相似文献
6.
Using the following notation: C is the space of continuous bounded functions f equipped with the norm
, V is the set of functions f such that
, the set E consists of fCV and possesses the following property:
is summable on each finite interval,
we establish some assertions similar to the following theorem: Let
0$$
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, Then for fV the series uniformly converges with respect to
and the following equality holds: This theorem develops some results obtained by Zubov relative to the approximation of probability distributions. Bibliography: 4 titles. 相似文献
7.
Let
be the Jacobi polynomials and let C[a,b] be the space of continuous functions on [ a,b] with the uniform norm. In this paper, we study sequences of Lebesgue constants, i.e., of the norms of linear operators
generated by a multiplier matrix
defined by the following relations: and In the case || = || = 1/2, we prove the following statements for the Jacobi polynomials (these statements are similar to known results for the trigonometrical system). Consider the cases
and Under some conditions on a function , the values
and
equal and In addition, we show that for the Fourier–Legendre summation methods ( = = 0) generated by the multiplier function
, the limit and supremum of the sequence of Lebesgue constants may differ. Bibliography: 11 titles. 相似文献
8.
Let S
k
( 0(N)) be the space of cusp forms of even weight k for
0
(N), let
be the set of all newforms in S
k
(
0
(N)), and let
be the symmetric square of the Hecke L-function of a form
. It is proved that for N=p we have where the -constant depends only on and k. Let f(z)S
k
(0(N)): The distribution of values of the sums for increasing X and N is studied. Bibliography: 13 titles. 相似文献
9.
Let u and solve the problem where is an open set in
0\} ,n \geqslant 2,H = \Delta - \partial _t \hfill \\ \hfill \\ \end{gathered} $$
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is the heat operator,
denotes the characteristic function of ,
is the unit cylinder in n+1,
, and the first equation is satisfied in the sense of distributions. We obtain the optimal regularity of the function u, i.e., we show that
. Bibliography: 6 titles. 相似文献
10.
In this work the authors study the conditions for the existence of diffusion equations in the cylinder Q = 3 D ×
+,
n
, satisfying the homogeneous Dirichlet or Neumann conditions on the side boundary of the cylinder Q and decreasing with respect to t as a power for t . 相似文献
11.
An analog of the classical Fourier formula for the characteristic function of a convex compact set
is considered: where W is a polyhedral in
. Bibliography: 6 titles. 相似文献
12.
Let
be the space of 2-periodic functions whose ( r – 1)th-order derivative is absolutely continuous on any segment and rth-order derivative belongs to L
p, S
2n,m
is the space of 2-periodic splines of order m of minimal defect over the uniform partition
. In this paper, we construct linear operators
such that where To construct the operators X
n,r,m, we use the same idea as in the polynomial case, i.e., the interpolation of Bernoulli kernels. As is proved, the operators X
n,r,m converge to polynomial Akhiezer–Krein–Favard operators as
. Bibliography: 10 titles. 相似文献
13.
Let
be the class number of properly equivalent primitive binary quadratic forms
of discriminant
. The case of indefinite forms
is considered. Assuming that the extended Riemann hypothesis for some fields of algebraic numbers holds, the following results are proved. 1. Let
be an arbitrarily slow monotonically increasing function such that
. Then |
(\log p)^{\alpha (p)} } \right\} = o(\pi (x)),$$
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where
. 2. Let F be an arbitrary sufficiently large positive constant. Then for
x_F$$
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, the relation |
F} \right\} \asymp \frac{{\pi (x)}}{F}$$
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holds. 3. The relation holds, where A is Artin's constant. Hence, for the majority of discriminants of the form
, where
, the class numbers are small. This is consistent with the Gauss conjecture concerning the behavior of
for the majority of discriminants
0$$
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in the general case. Bibliography: 22 titles. 相似文献
14.
The following classes of functions analytic in the unit disk are considered: and where
is the Nevanlinna characteristic and
is a properly changing positive function on (0,1]. Necessary and sufficient conditions on
are established under which the classes
and
are invariant under the operators of differentiation and integration. Bibliography: 7 titles. 相似文献
15.
Let
. Assume that V is a manifold,
is the set of germs of n-dimensional oriented submanifolds of V, and
is the 2-module of all 2-valued functions on E
n
(V). If
is an oriented submanifold, let
be the indicator function of the set of germs of X. It is proved that there exists a quadratic map
such that for any compact oriented submanifold
one has the relation
, where
is the (rational) semicharacteristic of
, i.e., the residue class defined by the formula Bibliography: 7 titles. 相似文献
16.
Let {\bold x}[] be a stationary Gaussian process with zero mean and spectral density f, let
be the -algebra induced by the random variables {\bold x}[], D(R 1), and let
t, t > 0, be the -algebra induced by the random variables x[],supp [-t,t]. Denote by
(f) the Gaussian measure on
generated by {\bold x}. Let
t(f) be the restriction of
(f) to
t. Let f and g be nonnegative functions such that the measures
t(f) and
t(g) are absolutely continuous. Put For a fixed g(u) and for f(u)= f t(u) close to g(u) in some sense, the asymptotic normality of
t(f,g) is proved under some regularity conditions. Bibliography: 14 titles. 相似文献
17.
Let C[-1,1] be the space of continuous functions f:[-1,1] with the uniform norm, let
Pk
be the Legendre polynomials such that
Pk
(1)=1, and let
J0
be the Bessel function of zero index. We consider sequences of linear operators (summation methods)
Un:C
[-1,1] C[-1,1] defined by a multiplier function as follows: The values
, the norms of the operators
Un
, are called the Lebesgue constants of a summation method. The main result of this paper is the following statement. If a function is continuous on [\0,+),
is the FourierBessel transform of , and the function
is summable on [\0,+) for some q>1, then Bibliography: 8 titles. 相似文献
18.
Let h(d) be the class number of properly equivalent primitive binary quadratic forms ax 2+bxy+cy 2 with discriminant d=b 2-4ac. The behavior of h(5p 2), where p runs over primes, is studied. It is easy to show that there are few discriminants of the form 5p 2 with large class numbers. In fact, one has the estimate |
x^{1 - \delta } \} \ll x^{2\delta } ,$$
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where is an arbitrary constant number in (0;1/2). Assume that (x) is a positive function monotonically increasing for x and (x). If , then (assuming the validity of the extended Riemann hypothesis for certain Dedekind zeta-functions) it is proved that |
\alpha (x)} \right\} \asymp \frac{{\pi (x)}}{{\alpha (x)}}.$$
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It is also proved that for an infinite set of p with
one has the inequality where log
k
p is the k-fold iterated logarithm ( k is an arbitrary integer, k3). Results on mean values of h(5p
2
) are also obtained. Similar facts are true for the residual indices of an integer a2 modulo p: where o(a,p) is the order of a modulo p. Bibliography: 13 titles. 相似文献
19.
A generalized interpolation polynomial with a base function
and node coefficients
, is a polynomial of the form where the system of functions
forms a Chebyshev system on [ a,b]. In this article, we show that by using the polynomials g( x) one can construct both adaptive quadrature formulas that optimize the quadrature error and piecewise-smooth stable solutions of the Cauchy problem. 相似文献
20.
In this article equations of the form are studied; here u( t) is a function with values in the Hilbert space
and the coefficients T
j
, j = 1,..., n are linear operators, possibly unbounded, in
. The operator symbol T() is assumed to be dissipative, that is, to satisfy the condition: Im( T() x, x) 0 for
and x
( T). When the space
is finite-dimensional, theorems of factorization for the symbol T() and theorems on the unique solvability for the truncated Cauchy problem on the half-axis t [0,) are proved. In the infinite-dimensional space we can obtain identities for solutions of the equations considered. From these identities it is possible to deduce a priori estimates for the solutions. 相似文献
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