The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems | Zendy

G. Isac | Zendy; M Cojocaru | Zendy

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The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems

Author(s) -

G. Isac,

M Cojocaru

Publication year - 2004

Publication title -

journal of function spaces

Language(s) - English

Resource type - Journals

eISSN - 2314-8896

pISSN - 2314-8888

DOI - 10.1155/2004/543714

Subject(s) - mathematics , hilbert space , projection (relational algebra) , representation (politics) , operator (biology) , differential operator , metric (unit) , pure mathematics , dynamical systems theory , derivative (finance) , rigged hilbert space , representation theorem , mathematical analysis , algebra over a field , reproducing kernel hilbert space , algorithm , biochemistry , chemistry , operations management , physics , repressor , quantum mechanics , politics , political science , transcription factor , financial economics , law , economics , gene

In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that this development is possible if we use the viable solutions of differential inclusions. We use also pseudomonotone operators

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