Conditional Positivity of Quadratic Forms in Hilbert Space

机译：Hilbert空间中二次型的条件正定性

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If X and Y are real Hilbert spaces (A : X approaches Y is a bounded linear operator, and gamma is contained in set Y is a closed convex cone) an immediate sufficient condition for a quadratic form Q on X to be positive subject to the constraint Ax is an element of gamma, is that Q be decomposable as a sum Q(x) = C(Ax) + S(x), where C is a quadratic form on Y which is positive on gamma, and S is positive definite on X. The necessity of such a decomposition is established for a class of quadratic forms which commonly occur in variational problems - the Legendre forms. The proof furnishes formulas for C and S which are explicit apart from the occurrence of an unkown scalar. The usefulness of the result is illustrated by the determination of the focal (conjugate) time of a linear-quadratic control problem with inequality constraints on the final state.

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作者
Martin, D. H.;
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年度 1979
页码 p.1-25
总页数 25
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Functionals; Hilbert space; Quadratic equations; Constraints; Legendre functions; Scalers;

机译：函数;希尔伯特空间;二次方程;约束;勒让德函数;定标器;

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2. On the number of representations of positive integers by quadratic forms as the basis of the spaceS4(Γ0(47),1) [J] . AhmetTekcan, OsmanB?z?m International journal of mathematics and mathematical sciences . 2004,第12期

机译：关于二次整数以空间S4（Γ0（47），1）为基础的表示形式的数量
3. Positive operators on certain spaces of quadratic forms [French] [J] . El Kadiri M. Linear Algebra and its Applications . 1998,第1a3期

机译：二次形的某些空间上的正算子[法语]
4. Method to Transform a Kind of Semi-positive Quadratic Problem into Positive Quadratic Problem [C] . Wang Mingyu International Conference on Electrical and Control Engineering . 2010

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5. Some contributions to analysis: A new space of generalized functions for integro-differential equations involving Hilbert transforms, and a note on the non-nuclearity of a space of test functions on Hilbert space. [D] . Donnelly, Roderick Kerry. 1988

机译：对分析的一些贡献：涉及Hilbert变换的积分微分方程的广义函数的新空间，以及关于Hilbert空间上测试函数的空间的非核性的注释。
6. Some means inequalities for positive operators in Hilbert spaces [O] . Jin Liang, Guanghua Shi -1

机译：希尔伯特空间中一些正算符的不等式
7. An approximation theory for elliptic quadratic forms on Hilbert spaces: Application to the eigenvalue problem for compact quadratic forms [O] . John Gregory 1971

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8. Quadratic Forms in Hilbert Spaces and Asymptotic Perturbation Series [R] . Tosio Kato 1955

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Conditional Positivity of Quadratic Forms in Hilbert Space

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