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191.
Genqi XU 《Frontiers of Mathematics in China》2022,17(1):47
This paper is a survey for development of linear distributed parameter system. At first we point out some questions existing in current study of control theory for the Lp linear system with an unbounded control operator and an unbounded observation operator, such as stabilization problem and observer theory that are closely relevant to state feedback operator. After then we survey briefly some results on relevant problems that are related to solvability of linear differential equations in general Banach space and semigroup perturbations. As a principle, we propose a concept of admissible state feedback operator for system (A, B). Finally we give an existence result of admissible state feedback operators, including semigroup generation and the equivalent conditions of admissibility of state feedback operators, for an Lp well-posed system. 相似文献
192.
An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail. 相似文献
193.
194.
Recently, we introduced a class of generalized hypergeometric functionsI
n:(b
q)/α:(a
p) (x, w) by using a difference operator Δ
x,w
, where
. In this paper an attempt has been made to obtain some bilateral generating relations associated withI
n
ga
(x, w). Each result is followed by its applications to the classical orthogonal polynomials. 相似文献
195.
J. A. Yan 《Applied Mathematics and Optimization》1995,31(2):137-153
Some sharp results about Weiner and Wick products of whitenoise functionals are obtained. Using the inequality of Wick products we show to what extent scaling transformations, translations, and Sobolev differentiations can be performed on white-noise functionals.This work was supported by the National Natural Science Foundation of China. This paper is an enlargement and revised version of the paper entitled Products and Transforms of White-Noise Functionals (preprint, 1990). 相似文献
196.
Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution
belongs to the range of the operator (T
*
T)
v
, o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India. 相似文献
197.
Fan Qihong 《数学年刊B辑(英文版)》1994,15(3):327-334
This paper coutinues the studies of the essential spectrum of nonsemi-bounded pseudodifferential operators. The author improves the results in [5] in some sense. For the relativistic Schrodinger operator,√(-Δ+m^2)+v(x),complete results are obtained. 相似文献
198.
给出 Banach空间列{Xi}i=1∞的 lp乘积B-凸的特征刻划, 证明B-凸空间上的每个黎斯算子可West分解,即分解成一个紧算子和一个拟幂 零算子的和. 相似文献
199.
Naihuan Jing 《Journal of Algebraic Combinatorics》1994,3(3):291-305
We derive a duality formula for two-row Macdonald functions by studying their relation with basic hypergeometric functions. We introduce two parameter vertex operators to construct a family of symmetric functions generalizing Hall-Littlewood functions. Their relation with Macdonald functions is governed by a very well-poised q-hypergeometric functions of type 43, for which we obtain linear transformation formulas in terms of the Jacobi theta function and the q-Gamma function. The transformation formulas are then used to give the duality formula and a new formula for two-row Macdonald functions in terms of the vertex operators. The Jack polynomials are also treated accordingly. 相似文献
200.
Best possibility of the Furuta inequality 总被引:5,自引:0,他引:5
Let , and . Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then . In this paper, we prove that the range and is best possible with respect to the Furuta inequality, that is, if or , then there exist which satisfy but .