# Integral representations of unbounded operators by infinitely smooth kernels

Open Mathematics (2005)

- Volume: 3, Issue: 4, page 654-665
- ISSN: 2391-5455

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topIgor Novitskiî. "Integral representations of unbounded operators by infinitely smooth kernels." Open Mathematics 3.4 (2005): 654-665. <http://eudml.org/doc/268926>.

@article{IgorNovitskiî2005,

abstract = {In this paper, we prove that every unbounded linear operator satisfying the Korotkov-Weidmann characterization is unitarily equivalent to an integral operator in L 2(R), with a bounded and infinitely smooth Carleman kernel. The established unitary equivalence is implemented by explicitly definable unitary operators.},

author = {Igor Novitskiî},

journal = {Open Mathematics},

keywords = {47G10; 45P05},

language = {eng},

number = {4},

pages = {654-665},

title = {Integral representations of unbounded operators by infinitely smooth kernels},

url = {http://eudml.org/doc/268926},

volume = {3},

year = {2005},

}

TY - JOUR

AU - Igor Novitskiî

TI - Integral representations of unbounded operators by infinitely smooth kernels

JO - Open Mathematics

PY - 2005

VL - 3

IS - 4

SP - 654

EP - 665

AB - In this paper, we prove that every unbounded linear operator satisfying the Korotkov-Weidmann characterization is unitarily equivalent to an integral operator in L 2(R), with a bounded and infinitely smooth Carleman kernel. The established unitary equivalence is implemented by explicitly definable unitary operators.

LA - eng

KW - 47G10; 45P05

UR - http://eudml.org/doc/268926

ER -

## References

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- [9] I.M. Novitskiî: “Reduction of linear operators in L 2 to integral form with smooth kernels”, Dokl. Akad. Nauk SSSR, Vol. 318(5), (1991), pp. 1088–1091; English transl.: Soviet Math. Dokl., Vol. 43(3), (1991), pp. 874–877.
- [10] I.M. Novitskiî: “Unitary equivalence between linear operators and integral operators with smooth kernels”, Differentsial’nye Uravneniya, Vol. 28(9), (1992), pp. 1608–1616; English transl.: Differential Equations, Vol. 28(9), (1992), pp. 1329–1337.
- [11] I.M. Novitskii: “Integral representations of linear operators by smooth Carleman kernels of Mercer type”, Proc. Lond. Math. Soc. (3), Vol. 68(1), (1994), pp. 161–177.
- [12] I.M. Novitskiî: “A note on integral representations of linear operators”, Integral Equations Operator Theory, Vol. 35(1), (1999), pp. 93–104. http://dx.doi.org/10.1007/BF01225530 Zbl0935.47024
- [13] I.M. Novitskiî: “Fredholm minors for completely continuous operators”, Dal’nevost. Mat. Sb., Vol. 7, (1999), pp. 103–122.
- [14] I.M. Novitskiî: “Fredholm formulae for kernels which are linear with respect to parameter”, Dal’nevost. Mat. Zh., Vol. 3(2), (2002), pp. 173–194.
- [15] I.M. Novitskiî: Simultaneous unitary equivalence to bi-Carleman operators with arbitrarily smooth kernels of Mercer type, arXiv:math.SP/0404228, April 12, 2004.
- [16] I.M. Novitskiî: Integral representations of closed operators as bi-Carleman operators with arbitrarily smooth kernels, arXiv:math.SP/0404244, April 13, 2004.
- [17] I.M. Novitskiî: Simultaneous unitary equivalence to Carleman operators with arbitrarily smooth kernels, arXiv:math.SP/0404274, April 15, 2004.
- [18] J. Weidmann: “Carlemanoperatoren”, Manuscripta Math., Vol. 2 (1970), pp. 1–38. http://dx.doi.org/10.1007/BF01168477

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