Indefinite least squares with a quadratic constraint

Regularization of an Indefinite Abstract Interpolation Problem with a Quadratic Constraint

Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its relationship with a linearly constrained interpolation problem is analyzed.

Representation Theorems for indefinite quadratic forms without spectral gap

The First and Second Representation Theorem for sign-indefinite quadratic forms are extended. We include new cases of unbounded forms associated with operators that do not necessarily have a spectral gap around zero. The kernel of the associated operators is determined for special cases. This extends results by Grubišić, Kostrykin, Makarov and Veselić in [Mathematika 59 (2013), 169--189].

Representation Theorems for Indefinite Quadratic Forms Revisited

The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring the second representation theorem to hold is proved. A new simple and explicit example of a self-adjoint operator for which the second representation theorem does not hold is also provided.

The TAN $2Θ$ Theorem for Indefinite Quadratic Forms

A version of the Davis-Kahan Tan $2Θ$ theorem [SIAM J. Numer. Anal. \textbf{7} (1970), 1 -- 46] for not necessarily semibounded linear operators defined by quadratic forms is proven. This theorem generalizes a recent result by Motovilov and Selin [Integr. Equat. Oper. Theory \textbf{56} (2006), 511 -- 542].

无限维耗散系统的最优控制

Optimal control of infinite-dimensional dissipative systems

研究无限维耗散系统线性二次最优控制问题，证明不定成本函数问题等价于非负成本函数问题，并建立值函数关系及Lur'e方程。

Krein空间中逼近问题的全局解

Global solutions of approximation problems in Krein spaces

本文研究Krein空间中不定加权最小二乘、抽象样条与平滑三类逼近问题，分析其对每点解的存在性、线性连续解算子的存在性及J-迹算子问题的可解性。