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Generalized selfadjoinness of differentiation operator on weight Hilbert spases

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Abstract

We consider examples of operators that act in some Hilbert rigging from positive Hilbert space into the negative one. For the first derivative operator we investigate a ``generalized'' selfadjointness in the sense of weight Hilbert riggings of the spaces $L^2([0,1])$ and $L^2(\mathbb{R})$. We will show that an example of the operator $i \frac{d}{dt}$ in some rigging scales, which is selfadjoint in usual case and not generalized selfadjoint, can not be constructed.


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Article Information

TitleGeneralized selfadjoinness of differentiation operator on weight Hilbert spases
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 4, 333-337
MathSciNet MR2374835
CopyrightThe Author(s) 2007 (CC BY-SA)

Authors Information

Ivan Ya. Ivasiuk
Department of Mathematical Analysis, National Taras Shevchenko University of Kyiv, Kyiv, Ukraine 


Citation Example

Ivan Ya. Ivasiuk, Generalized selfadjoinness of differentiation operator on weight Hilbert spases, Methods Funct. Anal. Topology 13 (2007), no. 4, 333-337.


BibTex

@article {MFAT429,
    AUTHOR = {Ivasiuk, Ivan Ya.},
     TITLE = {Generalized selfadjoinness of differentiation operator on weight Hilbert spases},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {333-337},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=429},
}


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