Geodesic
On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2014) no. 2, pp. 163-188 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We define the families of maximal and minimal relations generated by an integral equation with a Nevanlinna operator measure in the infinite-dimensional case and prove their holomorphic property. We show that if the restrictions of maximal relations are continuously invertible, then the operators inverse to these restrictions are integral. By using these results, we prove the existence of the characteristic operator and describe the families of linear relations generating the characteristic operator. 
@article{JMAG_2014_10_2_a0,
     author = {V. M. Bruk},
     title = {On the {Characteristic} {Operator} of an {Integral} {Equation} with a {Nevanlinna} {Measure} in the {Infinite-Dimensional} {Case}},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {163--188},
     year = {2014},
     volume = {10},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2014_10_2_a0/}
}
TY  - JOUR
AU  - V. M. Bruk
TI  - On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2014
SP  - 163
EP  - 188
VL  - 10
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JMAG_2014_10_2_a0/
LA  - en
ID  - JMAG_2014_10_2_a0
ER  - 
%0 Journal Article
%A V. M. Bruk
%T On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2014
%P 163-188
%V 10
%N 2
%U http://geodesic.mathdoc.fr/item/JMAG_2014_10_2_a0/
%G en
%F JMAG_2014_10_2_a0
V. M. Bruk. On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2014) no. 2, pp. 163-188. http://geodesic.mathdoc.fr/item/JMAG_2014_10_2_a0/

[1] Math. Notes, 66:6 (1999), 741–753 | DOI | DOI | MR | Zbl

[2] F. S. Rofe-Beketov, “Square-Integrable Solutions, Self-Adjoint Extensions and Spectrum of Differential Systems”, Differential Equations, Proc. from the Uppsala 1977 Intern. Conf. on Differ. Equations (Uppsala, 1977), 169–178 | MR | Zbl

[3] Russian Mathem. Surv., 63:1 (2008), 109–153 | DOI | DOI | MR | Zbl

[4] V. I. Khrabustovsky, “On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. 1: General case”, J. Math. Phys., Anal., Geom. series 2, 2006, no. 2, 149–175 ; “2: Abstract Theory”, no. 3, 299–317 ; “3: Separated Boundary Conditions”, no. 4, 449–473 | MR | Zbl | MR | Zbl | MR | Zbl

[5] V. I. Khrabustovsky, “On Characteristic Matrix of Weil-Titchmarsh Type for Differential-Operator Equations which Contains the Spectral Parameter in Linearly or Nevanlinna's Manner”, Mat. Fiz., Anal., Geom., 10:2 (2003), 205–227 | MR

[6] V. M. Bruk, “On Linear Relations Generated by a Differential Expression and by a Nevanlinna Operator Function”, J. Math. Phys., Anal., Geom. series 7, 2011, no. 2, 115–140 | MR | Zbl

[7] Rus. Mathem., 56:10 (2012), 1–14 | DOI | MR | Zbl

[8] Rus. Mathem., 57:2 (2013), 13–24 | DOI | MR | Zbl

[9] Yu. M. Berezanski, Expansions in Eigenfunctions of Selfadjoint Operators, Amer. Math. Soc., Providence, RI, 1968 ; Russian edition, Naukova Dumka, Kiev, 1965 | MR | Zbl

[10] Math. Notes, 24:4 (1979), 767–773 | DOI | MR | Zbl

[11] V. I. Gorbatchuk, M. L. Gorbatchuk, Boundary Value Problems for Differential Operator Equations, Kluwer Acad. Publ., Dordrecht–Boston–London, 1991; Russian edition, Naukova Dumka, Kiev, 1984

[12] J.-L. Lions, E. Magenes, Problemes aux Limites non Homogenes et Applications, Dunod, Paris, 1968

[13] Funct. Anal. and Appl., 36:2 (2002), 154–158 | DOI | DOI | MR | Zbl

[14] Izv. Math., 73:2 (2009), 215–278 | DOI | DOI | MR | Zbl

[15] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin–Heidelberg–New York, 1966 | MR | Zbl

[16] V. M. Bruk, “On Invertible Restrictions of Closed Operators in Banach Spaces”, Funct. Anal., 28, Uljanovsk), 1988, 17–22 (Russian) | MR | Zbl

[17] H. Schaefer, Topological Vector Spaces, The Macmillan Company, New York; Collier-Macmillan Limited, London, 1966 | MR | Zbl

[18] V. M. Bruk, “Generalized Resolvents of Symmetric Relations Generated on Semi-Axis by a Differential Expression and a Nonnegative Operator Function”, J. Math. Phys., Anal., Geom., 2:4 (2006), 372–387 | MR | Zbl

[19] A. V. Strauss, “Generalized Resolvents of Symmetric Operators”, Izv. Akad. Nauk SSSR, Ser. Mat., 18 (1954), 51–86 (Russian) | MR

[20] A. Dijksma, H. S. V. de Snoo, “Self-adjoint Extensions of Symmetric Subspaces”, Pacific J. Math., 54:1 (1974), 71–100 | DOI | MR | Zbl

[21] Math. Notes, 17:1 (1975), 25–28 | DOI | MR

[22] Math. USSR-Sb., 29:2 (1976), 186–192 | DOI | MR | Zbl

[23] Soviet. Math. Dokl., 10:1 (1969), 188–192 | MR | Zbl

[24] F. S. Rofe-Beketov, A. M. Khol'kin, Spectral Analysis of Differential Operators. Interplay between Spectral and Oscillatory Properties, World Sci. Monogr. Ser. Math., 7, Singapore, 2005 | DOI | MR | Zbl