scholarly journals Sesquilinear forms associated to sequences on Hilbert spaces

2019 ◽  
Vol 189 (4) ◽  
pp. 625-650 ◽  
Author(s):  
Rosario Corso
Keyword(s):  
Hilbert Spaces ◽  
Sesquilinear Forms

Sesquilinear Forms in Hilbert Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Symmetric Operator ◽  
Important Application ◽  
Sectorial Operator ◽  
Friedrichs Extension ◽  
Sesquilinear Forms ◽  
Variational Solutions ◽  
Sesquilinear Form ◽  
Densely Defined

The centre-pieces of this chapter are the Lax–Milgram Theorem and the existence of weak or variational solutions to problems involving sesquilinear forms. An important application is to Kato’s First Representation Theorem, which associates a unique m-sectorial operator with a closed, densely defined sesquilinear form, thus extending the Friedrichs extension for a lower bounded symmetric operator. Stampacchia’s generalization of the Lax–Milgram Theorem to variational inequalities is also discussed.

Gaussian Hilbert Spaces

1997 ◽  
Author(s):  
Svante Janson
Keyword(s):  
Hilbert Spaces

On split equality monotone Yosida variational inclusion and fixed point problems for countable infinite families of certain nonlinear mappings in Hilbert spaces

2020 ◽  
Vol Accepted ◽  
Author(s):  
Oluwatosin Temitope Mewomo ◽  
Hammed Anuoluwapo Abass ◽  
Chinedu Izuchukwu ◽  
Olawale Kazeem Oyewole
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Variational Inclusion ◽  
Nonlinear Mappings

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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