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1.
E. G. Goluzina 《Journal of Mathematical Sciences》2002,110(6):3052-3057
Let
be the class of functions satisfying the following conditions: these functions are regular and typically real in the unit disk, they have the form
, and the equality
holds for some fixed
and
with
. We find the set of values of the first two coefficients for functions from this class. Boundary functions for these sets of values are found. Some previous results of the author are supplemented. Boundary functions for the sets of values for the functionals
and
in the class
are found. Bibliography: 5 titles. 相似文献
2.
V. V. Kornienko 《Mathematical Notes》2000,68(5-6):576-587
We study the distribution in the complex plane
of the spectrum of the operator
, generated by the closure in
of the operation
originally defined on smooth functions
with values in a Hilbert space
satisfying the Dirichlet conditions
. Here
and A is a model operator acting in
. Criterial conditions on the parameter
for the eigenfunctions of the operator
to form a complete and minimal system as well as a Riesz basis in the Hilbert space H are given. 相似文献
3.
We study the asymptotic invertibility as
of matrices of the form
and
, where a and b are functions defined on the sets
. The joint asymptotic behavior of the spectrum of these matrices is analyzed. 相似文献
4.
Tomasz Człapiński 《Czechoslovak Mathematical Journal》1999,49(4):791-809
We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order
where
is a function defined by z
(x,y)(t, s) = z(x + t, y + s), (t, s) [–, 0] × [0, h]. Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem. 相似文献
5.
We obtain sufficient conditions for the continuity of the general nonlinear superposition operator (generalized Nemytskii operator) acting from the space
of differentiable functions on a bounded domain
to the Lebesgue space
. The values of operators on a function
are locally determined by the values of both the function
itself and all of its partial derivatives up to order
inclusive. In certain particular cases, the sufficient conditions obtained are proved to be necessary as well. The results are illustrated by several examples, and an application to the theory of Sobolev spaces is also given. 相似文献
6.
The problem on the existence of a positive in the interval ]a, b[ solution of the boundary value problem
is considered, where the functions f and
satisfy the local Carathéodory conditions. The possibility for the functions f and g to have singularities in the first argument (for t = a and t = b) and in the phase variable (for u = 0) is not excluded. Sufficient and, in some cases, necessary and sufficient conditions for the solvability of that problem are established. 相似文献
7.
Subdifferentials with respect to dualities 总被引:1,自引:0,他引:1
Juan-Enrique Martinez-Legaz Ivan Singer 《Mathematical Methods of Operations Research》1995,42(1):109-125
LetX andW be two sets and: ¯RX ¯RW a duality (i.e., a mapping
such that
for all
and all index setsI). We introduce and study the subdifferential
of a function
at a pointx
o
X, with respect to. We also consider the particular cases when is a (Fenchel-Moreau) conjugation, or a -duality, or a -duality, in the sense of [8]. 相似文献
8.
Let S be a real interval with
, and
be a function satisfying
We show that if h is Lebesgue or Baire measurable, then there
exists
such that
That result is motivated by a question of E. Manstaviius.
Received: 11 February 2003 相似文献
9.
The systems of bases are constructed for the spaces of cusp forms
and
. Formulas are obtained for the number of representations of a positive integer by the sum of k binary quadratic forms of the kind
, of the kind
and of the kind
. 相似文献
10.
O. L. Vinogradov 《Journal of Mathematical Sciences》2001,107(4):3987-4001
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
11.
Michael Reid 《Compositio Mathematica》2003,137(1):75-90
A refinement of the rank 1 Abelian Stark conjecture has been formulated by B.Gross. This conjecture predicts some
-adic analytic nature of a modification of the Stark unit. The conjecture makes perfect sense even when
is an Archimedean place. Here we consider the conjecture when
is a real place, and interpret it in terms of 2-adic properties of special values of L-functions. We prove the conjecture for CM extensions; here the original Stark conjecture is uninteresting, but the refined conjecture is nontrivial. In more generality, we show that, under mild hypotheses, if the subgroup of the Galois group generated by complex conjugations has less than full rank, then the refined conjecture implies that the Stark unit should be a square. This phenomenon has been discovered by Dummit and Hayes in a particular type of situation. We show that it should hold in much greater generality. 相似文献
12.
Using a multidimensional analogue of Vinogradov's inequality for a trigonometric integral, the upper bounds are constructed for the moduli of the characteristic functions both of the system of monomials in components of a random vector with an absolutely continuous distribution in
and of the system
where
is uniformly distributed in [0, l]s. 相似文献
13.
In this paper, we consider equations of the form
, where
is a function with values in the Hilbert space
, the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in
. The linear operator
generating the C
0-semigroup in the energy space
is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms. 相似文献
14.
We establish conditions for the stabilizability of evolution systems of partial differential equations on
by one-dimensional feedback controls. To prove these conditions, we use the Fourier-transform method. We obtain estimates for semialgebraic functions on semialgebraic sets by using the Tarski–Seidenberg theorem and its corollaries. We also give examples of stabilizable and nonstabilizable systems. 相似文献
15.
N. Yu. Galanova 《Algebra and Logic》2003,42(1):14-19
Let
be a field of formal power series with real coefficients, whose supports are well ordered subsets of an Abelian group
of cardinality strictly less than
. For
, we give criteria of a section being symmetric and of a symmetric section being Dedekind. It is proved that an
-saturated non-standard real line
is isomorphic to some field of the form
. For
, some consequences are inferred regarding symmetric sections, and the cofinality of banks of the sections. 相似文献
16.
Let
and
be Hausdorff topological vector spaces over the field
, let
be a bilinear functional, and let
be a non-empty subset of
. Given a set-valued map
and two set-valued maps
, the generalized bi-quasi-variational inequality (GBQVI) problem is to find a point
and a point
such that
and
for all
and for all
or to find a point
a point
and a point
such that
and
for all
. The generalized bi-quasi-variational inequality was introduced first by Shih and Tan [8] in 1989. In this paper we shall obtain some existence theorems of generalized bi-quasi-variational inequalities as application of upper hemi-continuous operators [4] in locally convex topological vector spaces on compact sets. 相似文献
17.
Let
be the local time process of a linear Brownian motion B. We integrate the Borel functions on
with respect to
. This allows us to write Itôrs formula for new classes of functions, and to define a local time process of B on any borelian curve. Some results are extended from deterministic to random functions. 相似文献
18.
Günter Mayer 《Applications of Mathematics》1998,43(4):241-254
For contractive interval functions [g] we show that
results from the iterative process
after finitely many iterations if one uses the epsilon-inflated vector
as input for [g] instead of the original output vector [x]
k
. Applying Brouwer's fixed point theorem, zeros of various mathematical problems can be verified in this way. 相似文献
19.
Mohamed Sifi 《Journal of Theoretical Probability》1995,8(3):475-499
We provide
相似文献
20.
Dr. K. Taubert 《Numerische Mathematik》1976,26(4):379-395
Summary In the present article we show that the solutions of initial value problems in ordinary differential equations with discontinuous right-hand side can be approximated by a slight modification of the Euler-Cauchy method. The method is succesfully applied to
and
for some initial values. By a solution of a differential equation with discontinuous right-hand side we mean the concept given by A. F. Filippov. 相似文献
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