Geodesic
Spectral decomposition of normal operator in real Hilbert space
Ufa mathematical journal, Tome 9 (2017) no. 4, pp. 85-96

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider normal unbounded operators acting in a real Hilbert space. The standard approach to solving spectral problems related with such operators is to apply the complexification, which is a passage to a complex space. At that, usually, the final results are to be decomplexified, that is, the reverse passage is needed. However, the decomplexification often turns out to be nontrivial. The aim of the present paper is to extend the classical results of the spectral theory for the case of normal operators acting in a real Hilbert space. We provide two real versions of the spectral theorem for such operators. We construct the functional calculus generated by the real spectral decomposition of a normal operator. We provide examples of using the obtained functional calculus for representing the exponent of a normal operator.
Keywords: unbounded normal operator, real Hilbert space, spectral theorem, functional calculus.
Mots-clés : complexification 
@article{UFA_2017_9_4_a8,
     author = {M. N. Oreshina},
     title = {Spectral decomposition of   normal operator in   real {Hilbert} space},
     journal = {Ufa mathematical journal},
     pages = {85--96},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2017_9_4_a8/}
}
TY  - JOUR
AU  - M. N. Oreshina
TI  - Spectral decomposition of   normal operator in   real Hilbert space
JO  - Ufa mathematical journal
PY  - 2017
SP  - 85
EP  - 96
VL  - 9
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UFA_2017_9_4_a8/
LA  - en
ID  - UFA_2017_9_4_a8
ER  - 
%0 Journal Article
%A M. N. Oreshina
%T Spectral decomposition of   normal operator in   real Hilbert space
%J Ufa mathematical journal
%D 2017
%P 85-96
%V 9
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UFA_2017_9_4_a8/
%G en
%F UFA_2017_9_4_a8
M. N. Oreshina. Spectral decomposition of   normal operator in   real Hilbert space. Ufa mathematical journal, Tome 9 (2017) no. 4, pp. 85-96. http://geodesic.mathdoc.fr/item/UFA_2017_9_4_a8/