Fourteenth Schoo l o n Operator s
in Functiona l Space s
Spectral Theor y
of Operator s
Recent Titles in This Series
149 V . S. Afraimovich, e t al., Thirtee n Paper s i n Algebra , Functiona l Analysis , Topology , an d
Probability, Translate d fro m th e Russia n
148 A . D. Aleksandrov, O . V. Belegradek, L . A. Bokut', an d Yu. L . Ershov, Editors ,
First Siberia n Winte r Schoo l in Algebra and Analysi s
147 I . G. Bashmakova, et al., Nin e Paper s from th e Internationa l Congres s of Mathematician s
1986
146 L . A. Aizenberg, et al., Fiftee n Paper s in Complex Analysi s
145 S . G. Dalalyan, et al., Eigh t Papers Translated fro m th e Russia n
144 S . D. Berman, et al., Thirtee n Paper s Translated fro m th e Russia n
143 V . A. Belonogov, et al., Eigh t Papers Translated fro m th e Russia n
142 M . B. Abalovich, et al., Te n Papers Translated fro m th e Russia n
141 Kh . Drashkovicheva , et al., Ordere d Set s and Lattice s
140 V . I. Bernik, et al., Eleve n Papers Translated fro m th e Russia n
139 A . Ya. Aizenshtat , et al., Ninetee n Paper s on Algebraic Semigroup s
138 I . V. Kovalishina and V. P. Potapov, Seve n Papers Translated fro m th e Russia n
137 V . I. Arnold, et al., Fourtee n Paper s Translated fro m th e Russia n
136 L . A. Aksent'ev, et al., Fourtee n Paper s Translated fro m th e Russia n
135 S . N. Artemov, et al., Si x Papers in Logic
134 A . Ya. Aizenshtat , et al., Fourtee n Paper s Translated fro m th e Russia n
133 R . R. Suncheleev, et al., Thirtee n Paper s in Analysis
132 I . G. Dmitriev, et al., Thirtee n Paper s in Algebra
131 V . A. Zmorovich, et al., Te n Papers in Analysis
130 M . M. Lavrent'ev, et al., One-dimensiona l Invers e Problems of Mathematical Physic s
129 S . Ya . Khavinson ; translate d b y D . Khavinson , Tw o Paper s o n Extrema l Problem s i n
Complex Analysis
128 I . K. Zhuk, et al., Thirtee n Paper s in Algebra and Number Theor y
127 P . L. Shabalin, et al., Eleve n Papers in Analysis
126 S . A. Akhmedov, et al., Eleve n Papers on Differential Equation s
125 D . V. Anosov, et al., Seve n Papers in Applied Mathematic s
124 B . P. Allakhverdiev, et al., Fiftee n Paper s on Functional Analysi s
123 V . G. Maz'ya, e t al., Ellipti c Boundary Valu e Problems
122 N . U. Arakelyan, et al., Te n Papers on Complex Analysi s
121 D . L. Johnson, Th e Kourovka Notebook: Unsolve d Problem s in Group Theor y
120 M . G. Krein and V. A. Jakubovic, Fou r Paper s on Ordinary Differentia l Equation s
119 V . A. Dem'janenko, et al., Twelv e Papers in Algebra
118 Ju . V . Egorov, et al., Sixtee n Papers on Differential Equation s
117 S . V . Bockarev , e t al. , Eigh t Lecture s Delivere d a t th e Internationa l Congres s o f
Mathematicians i n Helsinki, 1 97 8
116 A . G. Kusnirenko, A. B. Katok, and V. M. Alekseev, Thre e Papers on Dynamical System s
115 I . S. Belov, et al., Twelv e Papers in Analysis
114 M . S . Birma n an d M . Z . Solomjak , Quantitativ e Analysi s i n Sobole v Imbeddin g
Theorems and Applications to Spectra l Theory
113 A . F. Lavrik, Twelv e Papers in Logic and Algebra
112 D . A. Gudkov and G. A. Utkin, Nin e Papers on Hilbert's 1 6t h Problem
111 V . M. Adamjan, et al., Nin e Papers on Analysis
110 M . S. Budjanu, et al., Nin e Papers on Analysis
(Continued in the back of this publication)
http://dx.doi.org/10.1090/trans2/150
American Mathematica l Societ y
TRANSLATIONS
Series 2 • Volum e 1 5 0
Soviet Regional Conference s
F o u r t e e n t h Schoo l o n Operator s
in Functiona l S p a c e s
Spectral Theor y
of Operator s
Novgorod State Pedagogica l Institut e
1989
S. G . Gindiki n
Editor
Translation edite d by SIMEON IVANO V
1991 Mathematics Subject Classification. Primar y 34L20 , 34L25 , 34L30 , 34L40 , 47A1 3 ,
47A40, 47H12; Secondary 58C40 .
Library o f Congres s Cataloging-in-Publication Dat a
School on Operators in Functional Spaces (14th: 1 989 : Novgorod State Pedagogical Institute)
Spectral theor y o f operators : proceeding s o f th e Fourteent h Schoo l o n Operator s i n
Functional Spaces , Novgorod Stat e Pedagogical Institute , 1 989/edito r S . G. Gindikin .
p. cm. - (America n Mathematical Societ y translations, ISSN 0065-9290; ser. 2, v. 1 50 .
Soviet regional conferences )
Translated fro m Russian .
Includes bibliographical references .
ISBN 0-821 8-7500- 0
1. Differential operators—Congresses . 2 . Spectral theory (Mathematics)—Congresses .
I. Gindikin , S . G . (Seme n Grigor'evich ) II . Title . III . Series : America n Mathematica l
Society translations; ser. 2, v. 1 50 . IV . Series: American Mathematical Societ y translations.
Soviet regional conferences .
QA3.A572 ser . 2 , vol. 1 5 0
[QA329.4]
510s-dc20 9 -4 69
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Contents
M. S. Birman and M. Z. Solomyak, Schrodinger operator. Estimate s fo r
number o f bound state s a s function-theoretical
1
proble m
D. G. Vasil'ev and Yu. G. Safarov, The asymptotic distribution o f eigenvalues of differentia l operator s 5
5
Yu. V. Egorov and V. A. Kondrat'ev, Estimates of the negative spectru m
of a n ellipti c operator
1
Yu. A. Kuperin and S. P. Merkur'ev, Selfadjoin t extension s an d scatter ing theory
1
fo r several-bod y system s 4 1
V
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Recent Titles in This Series
(Continued from the front of this publication)
109 D . V . Anosov , e t al. , Twent y Lecture s Delivere d a t th e Internationa l Congres s o f
Mathematicians i n Vancouver, 1 97 4
108 Ja . L . Geronimus and Gabor Szego, Tw o Papers on Special Function s
107 A . P. Misina and L. A. Skornjakov, Abelia n Group s and Module s
106 M . Ja. Antonovskii , V. G. Boltjanskii, an d T. A. Sarymsakoy, Topologica l Semifield s an d
Their Applications to General Topolog y
105 R . A . Aleksandrjan , e t al. , Partia l Differentia l Equations , Proceeding s o f a Symposiu m
Dedicated t o Academician S . L. Sobolev
104 L . V. Ahlfors, et al., Som e Problems o n Mathematics an d Mechanics , On the Occasion o f
the Seventieth Birthda y o f Academician M . A. Lavrent'ev
103 M . S. Brodskii, et al., Nin e Papers in Analysis
102 M . S. Budjanu, et al., Te n Papers in Analysis
101 B . M. Levitan, V. A. Marcenko, and B. L. Rozdestvenskii, Si x Papers in Analysis
100 G . S. Ceitin, et al., Fourtee n Paper s on Logic, Geometry, Topolog y and Algebra
99 G . S. Ceitin, et al., Fiv e Papers on Logic and Foundation s
98 G . S. Ceitin, et al., Fiv e Papers on Logic and Foundation s
97 B . M. Budak, et al., Eleve n Papers on Logic, Algebra, Analysis and Topolog y
96 N . D. Filippov, et al., Te n Papers on Algebra and Functiona l Analysi s
95 V . M. Adamjan, et al., Eleve n Papers in Analysis
94 V . A. Baranskii, et al., Sixtee n Papers on Logic and Algebra
93 Ju . M . Berezanskii, et al., Nin e Papers on Functional Analysi s
92 A . M. Ancikov, et al., Seventee n Paper s on Topology and Differentia l Geometr y
91 L . I. Barklon, et al., Eightee n Paper s on Analysis and Quantu m Mechanic s
90 Z . S. Agranovic, et al., Thirtee n Paper s on Functional Analysi s
89 V . M. Alekseev, et al., Thirtee n Paper s on Differential Equation s
88 1 .1 . Eremin, et al., Twelv e Papers on Real and Complex Functio n Theor y
87 M . A . Aizerman , e t al. , Sixtee n Paper s o n Differentia l an d Differenc e Equations ,
Functional Analysis, Games and Contro l
86 N . I. Ahiezer, e t al., Fiftee n Paper s o n Rea l an d Comple x Functions,* * Series, Differentia l
and Integral Equation s
85 V . T. Fomenko, et al., Twelv e Papers on Functional Analysi s and Geometr y
84 S . N. Cernikov, et al., Twelv e Papers on Algebra, Algebraic Geometry an d Topolog y
83 I . S. Arson, et al., Eightee n Paper s on Logic and Theory o f Function s
82 A . P. Birjukov, et al., Sixtee n Papers on Number Theory an d Algebr a
81 K . K . Golovkin , V . P . II 7 in, an d V . A . Solonnikov , Fou r Paper s o n Function s o f Rea l
Variables
80 V . S. Azarin, et al., Thirtee n Paper s on Functions of Real and Comple x Variable s
79 V . I. Arnol'd, et al., Thirtee n Paper s on Functional Analysi s and Differential Equation s
78 A . V. Arhangel'skii, et al., Eleve n Papers on Topolog y
77 L . A. Balasov, et al., Fourtee n Paper s on Series and Approximatio n
76 Gen g Ji, et al., Thirtee n Paper s on Algebra and Analysi s
75 A . A. Andronov, et al., Seve n Papers on Equation s Relate d t o Mechanics and Hea t
74 B . F. Bylov, et al., Te n Papers on Analysi s
73 V . P. Kompaniec, et al., Fourtee n Paper s on Algebra, Topology, Algebraic and Differentia l
Geometry
72 S . A. Akopjan, et al., Fiftee n Paper s on Analysis
(See the AMS catalogue fo r earlie r titles )
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