共查询到20条相似文献,搜索用时 171 毫秒
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Dongrui Wan 《Mathematische Nachrichten》2019,292(5):1161-1173
In this paper, we give an equivalent characterization of the domain of definition for the quaternionic Monge–Ampère operator, by using the theory of quaternionic closed positive current we established in [17–19]. This domain of definition for the complex Monge–Ampère operator was introduced by Blocki [7,8]. 相似文献
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Vladimir Ryzhov 《Integral Equations and Operator Theory》2008,60(4):539-571
We construct the symmetric functional model of an arbitrary closed operator with non-empty resolvent set acting on a separable
Hilbert space. The construction is based on the explicit form of the Sz.-Nagy-Foiaş model of a closed dissipative operator,
the Potapov-Ginzburg transform of characteristic functions, and certain resolvent identities. All considerations are carried
out under minimal assumptions, and obtained results are directly applicable to problems typically arising in mathematical
physics. Explicit formulae for all the objects participating in the model construction are provided.
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In this paper, the long time behavior of the dissipative generalized (2+1)-dimensional long–short wave equations was studied in dynamics. By applying projecting operator and the eigenvalue methods, the approximate inertial manifolds were constructed. And it is proved that arbitrary trajectory of the dissipative generalized (2+1)-dimensional long–short wave equations goes into a small neighborhood of the approximate inertial manifolds after long time. 相似文献
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S. V. Panyushkin 《Mathematical Notes》2006,79(3-4):537-550
We consider the generalized Fourier transform treated as an operator on the dual of an arbitrary locally convex space. We give a definition of this operator and establish its basic properties. Special attention is paid to cases in which the range of the generalized Fourier transform coincides with a weighted space of entire functions. The results are applied to finding the orders and types of operators in various spaces. 相似文献
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In this paper, we first give a simple proof of the decomposition theorem in Alber (Field Inst. Comm. 25 (2000) 77) and then present a new decomposition of arbitrary elements in reflexive strictly convex and smooth Banach spaces. As applications of the decomposition theorem, we give the representations of the metric projection operator for some kind of closed convex sets. Finally, we provide a sufficient condition under which the generalized projection operator coincides with the metric projection operator. 相似文献
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Generalized Fourier transform on an arbitrary triangular domain 总被引:4,自引:0,他引:4
In this paper, we construct generalized Fourier transform on an arbitrary triangular domain via barycentric coordinates and PDE approach. We start with a second-order elliptic differential operator for an arbitrary triangle which has the so-called generalized sine (TSin) and generalized cosine (TCos) systems as eigenfunctions. The orthogonality and completeness of the systems are then proved. Some essential convergence properties of the generalized Fourier series are discussed. Error estimates are obtained in Sobolev norms. Especially, the generalized Fourier transforms for some elementary polynomials and their convergence are investigated.
This work was supported by the Major Basic Project of China (No. G19990328) and National Natural Science Foundation of China (No. 60173021). 相似文献
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In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For arbitrary self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed
expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector
space, the endomorphism encoding the self-adjoint extension chosen. For particular examples, like the Friedrich’s extension,
the answer is easily extracted from the general result. In combination with (Bordag et al. in Commun. Math. Phys. 182(2):371–393,
1996), a closed expression for the determinant of an arbitrary self-adjoint extension of the full Laplace-type operator on
the generalized cone can be obtained. 相似文献
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Let D be a bounded convex domain of the complex plane. We study the problem of whether the fundamental principle holds for analytic function spaces on D invariant with respect to the differentiation operator and admitting spectral synthesis. Earlier this problem was solved under a restriction on the multiplicities of the eigenvalues of the differentiation operator. In the present paper, we lift this restriction. Thus, we present a complete solution of the fundamental principle problem for arbitrary nontrivial closed invariant subspaces admitting spectral synthesis on arbitrary bounded convex domains. 相似文献
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In the present work we show that the local generalized monotonicity of a lower semicontinuous set-valued operator on some certain type of dense sets ensures the global generalized monotonicity of that operator. We achieve this goal gradually by showing at first that the lower semicontinuous set-valued functions of one real variable, which are locally generalized monotone on a dense subsets of their domain are globally generalized monotone. Then, these results are extended to the case of set-valued operators on arbitrary Banach spaces. We close this work with a section on the global generalized convexity of a real valued function, which is obtained out of its local counterpart on some dense sets. 相似文献
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V. M. Bruk 《Mathematical Notes》1974,16(5):1079-1084
A self-adjoint second-order differential expression with an unbounded operator coefficient is considered in the space of vector functions. The domain of definition of the minimum and maximum operators generated by this expression is investigated, it is shown that any generalized resolvent of the minimum operator is an integral operator, and expansion in eigenfunctions is performed. 相似文献
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We investigate one class of perturbations of a closed densely-defined operator in a Hilbert space. These perturbations change the domain of definition of the operator. We prove that the perturbed operator S is closed and densely defined. We construct the adjoint operator S*. 相似文献
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《Nonlinear Analysis: Hybrid Systems》2007,1(3):383-397
In this paper we consider the uniform stabilization of a vibrating string with Neumann-type boundary conditions. Herein we do not consider a controller stabilizing the system, but emphasize the simplicity and effectiveness of the controller. We adopt the linear feedback control law, which comprises both boundary velocity and position, and prove that the closed loop system is dissipative and asymptotically stable. By asymptotic analysis of frequency of the closed loop system, we give asymptotic expression of the frequencies and the Riesz basis property of eigenvectors and generalized eigenvectors of the system operator under some conditions, and hence obtain the exponential stability of the closed loop system. We show that, for a particular case, the system may be super-stable in subspace of a codimensional one. From the above result, we conclude that one can design a much simpler linear controller by choice of parameters such that the closed loop system is of Riesz basic properties and exponentially stable. 相似文献
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Virginia V. Jory 《Numerical Functional Analysis & Optimization》2013,34(4):477-492
Let H1 and H2 be Hilbert spaces and let B be a closed linear operator mapping a dense subset of H1 into H2. Several families of approximators which converge t o the orthogonal or Moore-Penrose generalized inverse B? are constructed. Additionally, the approximators are shown t o provide regularization operators for the equation Bx=y. Some of the results are extended to dissipative operators on reflexive and general Banach spaces. 相似文献
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设■是复Hilbert空间,■是■上有界线性算子全体,■是标准算子代数且对于伴随运算封闭.本文结合广义Jensen等式证明了标准算子代数■上的和导子有关的函数方程具有广义Hyers-Ulam-Rassias稳定性. 相似文献
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Pickands coordinates were introduced as a crucial tool for the investigation of bivariate extreme value models. We extend their definition to arbitrary dimensions and, thus, we can generalize many known results for bivariate extreme value and generalized Pareto models to higher dimensions and arbitrary extreme value margins.In particular we characterize multivariate generalized Pareto distributions (GPs) and spectral δ-neighborhoods of GPs in terms of best attainable rates of convergence of extremes, which are well-known results in the univariate case. A sufficient univariate condition for a multivariate distribution function (df) to belong to the domain of attraction of an extreme value df is derived. Bounds for the variational distance in peaks-over-threshold models are established, which are based on Pickands coordinates. 相似文献
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A. N. Bogolubov M. D. Malykh Yu. V. Mukhartova 《Computational Mathematics and Mathematical Physics》2006,46(12):2129-2135
It is shown that the generalized Fourier transform can be extended to an arbitrary elliptic operator in a cylindrical domain with a Robin boundary condition. In this case, the existence of the Fourier image is a completely correct radiation condition determining a solution to the problem that is a superposition of waves traveling away from the source. 相似文献
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O. H. Storozh 《Journal of Mathematical Sciences》2010,170(5):580-587
In terms of abstract boundary conditions, we have established the connection between resolvents of two maximal dissipative
extensions of a symmetric operator with arbitrary defect numbers acting in a Hilbert space. In particular, the criterion of
resolvent comparability of the operators under consideration has been proved. 相似文献