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1.
《Comptes Rendus Mathematique》2014,352(7-8):651-654
We consider the functional generalized linear model whose response function is a linear operator depending on an explanatory variable X belonging to a functional space. It has been studied, among others, by Cardot and Sarda [4]. In this paper, we consider the functional generalized linear model with derivative component, denoted MLGFD in the following, whose response function depends on a linear operator of X and on its derivative. We propose estimators for the unknown functional parameters and provide convergence rates. 相似文献
2.
We consider linear boundary value problems for operator equations with generalized-invertible operator in a Banach or Hilbert space. We obtain solvability conditions for such problems and indicate the structure of their solutions. We construct a generalized Green operator and analyze its properties and the relationship with a generalized inverse operator of the linear boundary value problem. The suggested approach is illustrated in detail by an example. 相似文献
3.
V. V. Napalkov A. U. Mullabaeva 《Proceedings of the Steklov Institute of Mathematics》2015,288(1):142-155
We use a generalized differentiation operator to construct a generalized shift operator, which makes it possible to define a generalized convolution operator in the space H(?). Next, we consider the characteristic function of this operator and introduce a generalized Laplace transform. We study the homogeneous equation of the generalized convolution operator, investigate its solvability, and consider the multipoint Vallée Poussin problem. 相似文献
4.
本文将Коровкин关于线性正算子序列和线性连续多项式算子序列逼近一元连续函数的主要结果推广到m维连续函数空间Cm(D). 相似文献
5.
We introduce a generalized Wiener measure associated with a Gaussian Markov process and define a generalized analytic operator-valued
function space integral as a bounded linear operator from L
p
into L
p^\prime
(1<p ≤ 2) by the analytic continuation of the generalized Wiener integral. We prove the existence of the integral for certain functionals
which involve some Borel measures. Also we show that the generalized analytic operator-valued function space integral satisfies
an integral equation related to the generalized Schr?dinger equation. The resulting theorems extend the theory of operator-valued
function space integrals substantially and previous theorems about these integrals are generalized by our results. 相似文献
6.
We introduce a generalized Wiener measure associated with a Gaussian Markov process and define a generalized analytic operator-valued
function space integral as a bounded linear operator from L
p
into L
p^\prime
(1<p ≤ 2) by the analytic continuation of the generalized Wiener integral. We prove the existence of the integral for certain functionals
which involve some Borel measures. Also we show that the generalized analytic operator-valued function space integral satisfies
an integral equation related to the generalized Schr?dinger equation. The resulting theorems extend the theory of operator-valued
function space integrals substantially and previous theorems about these integrals are generalized by our results. 相似文献
7.
Yu. I. Petunin 《Ukrainian Mathematical Journal》1996,48(9):1460-1464
We introduce a new concept of generalized solution of operator equations with closed linear operator in a Banach space as
an element of the completion of the space in certain locally convex topology. We prove a theorem on the existence and uniqueness
of a generalized solution and give examples of finding the generalized solution for infinite systems of the linear algebraic
equations.
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 48, No. 9. pp. 1286–1290, September, 1996. 相似文献
8.
9.
We define a new notion of a generalized solution of an operator equation with a closed linear operator in a Banach space as
an element of the completion of this space with respect to some locally convex topology. We prove a theorem on the existence
and uniqueness of the generalized solution. Bibliography: 5 titles.
Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 93–99. 相似文献
10.
S. M. Chuiko 《Russian Mathematics (Iz VUZ)》2016,60(8):64-73
We find necessary and sufficient conditions for solvability and the construction of the generalized Green operator for Noetherian linear boundary-value problem for a linear matrix differential equation. We propose an operator, which leads a linear matrix algebraic equation to the traditional linear algebraic system with a rectangular matrix. We use pseudoinverseMoore–Penrose matrices and orthogonal projections for solving a linear algebraic system. 相似文献
11.
S. M. Chuiko 《Russian Mathematics (Iz VUZ)》2018,62(4):74-85
We find solvability conditions and give a construction of generalized Green operator for a linear matrix boundary-value problem. We suggest an operator which reduces a linear matrix equation to a standard linearNoetherian boundary-value problem. To solve a linearmatrix systemwe use an operatorwhich reduces a linear matrix equation to a linear algebraic equation with rectangular matrix. 相似文献
12.
Let T be a differential operator in a Hilbert space generated by a first-order infinite system of an ordinary linear differential expression, which is subject to infinitely many boundary conditions. We solve completely for y from Ty = g. The main tools involved are operator parts of closed linear manifolds, which are closely related to generalized inverses. 相似文献
13.
14.
非线性方程分歧理论中广义Lyapunov-Schmidt过程及应用 总被引:1,自引:0,他引:1
本文讨论带有参数的算子方程 f ( x,λ) =0的分歧问题 ,其中 f :X×Λ→ Y,X,Y为 Banach空间 ,Λ =R为参数空间 .利用 A =f′x( x0 ,λ0 )的有界线性广义逆 A+ ,引入广义 Lyapunov-Schmidt过程 ,当 A为 Fredholm算子时 ,这种广义 Lyapunov-Schmidt过程就成为通常的 Lyapunov-Schmidt过程 .本文利用所引进的广义Lyapunov-Schmidt过程 ,证得关于抽象方程 f ( x,λ) =0的一个分歧定理 . 相似文献
15.
《Journal of Approximation Theory》2005,132(1):34-41
Using local interpolation of Whitney functions, we generalize the Pawłucki and Pleśniak approach to construct a continuous linear extension operator. We show the continuity of the modified operator in the case of generalized Cantor-type sets without Markov's Property. 相似文献
16.
B. O. Vasilevskiĭ 《Siberian Mathematical Journal》2013,54(6):994-1004
We consider a regular Riemann surface of finite genus and “generalized spectral data,” a special set of distinguished points on it. From them we construct a discrete analog of the Baker-Akhiezer function with a discrete operator that annihilates it. Under some extra conditions on the generalized spectral data, the operator takes the form of the discrete Cauchy-Riemann operator, and its restriction to the even lattice is annihilated by the corresponding Schrödinger operator. In this article we construct an explicit formula for the Green’s function of the indicated operator. The formula expresses the Green’s function in terms of the integral along a special contour of a differential constructed from the wave function and the extra spectral data. In result, the Green’s function with known asymptotics at infinity can be obtained at almost every point of the spectral curve. 相似文献
17.
We propose an approach to the investigation of generalized solutions of linear operators that satisfy weakened a priori inequalities.
This approach generalizes several well-known definitions of generalized solutions of operator equations. We prove existence
and uniqueness theorems for a generalized solution. 相似文献
18.
We prove a Kantorovich-type theorem on the existence and uniqueness of the solution of a generalized equation of the form
f(u)+g(u) ' 0f(u)+g(u)\owns 0 where f is a Fréchet-differentiable function and g is a maximal monotone operator defined on a Hilbert space. The depth and scope of this theorem is such that when we specialize
it to nonlinear operator equations, variational inequalities and nonlinear complementarity problems we obtain novel results
for these problems as well. Our approach to the solution of a generalized equation is iterative, and the solution is obtained
as the limit of the solutions of partially linearized generalized Newton subproblems of the type Az+g(z) ' bAz+g(z)\owns b where A is a linear operator. 相似文献
19.
Michael Plum 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1991,42(6):848-863
Summary We derive bounds for the firstN eigenvalues of a linear second-order elliptic differential operator on a bounded domain, subject to mixed boundary conditions. The results are achieved by a combination of (a generalized version of) Kato's estimates and a homotopy algorithm. 相似文献