Publication Details:
Journal or Publication Title:
Armenian Journal of Mathematics=Հայկական մաթեմատիկական հանդես
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Title:
On Nagy-Foias Characteristic Function in Extensions Theory of Hermitian Operators
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Գլխ. խմբ.՝ Անրի Ներսեսյան ; Պատ. խմբ.՝ Լինդա Խաչատրյան ; Խմբ. տեղակալ՝ Ռաֆայել Բարխուդարյան
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Abstract:
For a densely defined in a Hilbert space closed Hermitian operator with infinite defect numbers its maximal extensions are discussed. The Nagy-Foias characteristic function of an arbitrary maximal dissipative extension is derived. Mutually complementary classes of such extensions, referred to as inherited and acquired are introduced, and the peculiarity of characteristic function, as determining the class of extensions it corresponds to, is noted. In the setting of Calkin's abstract boundary conditions theory abstract analogs of Nagy-Foias and Weyl functions are presented in similar manner, as operator functions involved in boundary operators, describing the class of inherited extensions. Existence and analyticity of these functions are proved.
Publisher:
National Academy of Sciences of Armenia
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General note:
Electronic Open Access Publication of the National Academy of Sciences of Armenia
Digitization:
ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան