Criteria for the Boundedness and Complete Continuity of Certain Imbedding Operators

  • V. L. Oleinik
  • B. S. Pavlov
Part of the Topics in Mathematical Physics book series (TOMP, volume 4)


The question of boundedness (compactness) of the imbedding of classes of smooth functions in a space of functions integrable with respect to some measure arises in many problems of spectral theory.


Singular Boundary Imbed Theorem Complete Continuity Special Sphere Finite Cardinality 
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Literature Cited

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    M. Sh. Birman, “On the spectrum of singular boundary value problems,” Matem. Sb., Vol. 55 (97), No. 2 (1961).MathSciNetGoogle Scholar
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    I. M. Glazman, Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators, Fizmatgiz, Moscow (1963).Google Scholar
  3. 3.
    M. Sh. Birman and B. S. Pavlov, “On the complete continuity of some imbedding operators,” Vesnik LGU, seriya mat., No. 1, Issue 1 (1961).Google Scholar
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    G. Hardy, J. Littlewood, and G. Polya, Inequalities, Second Ed., Cambridge (1954).Google Scholar
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    V. I. Smirnov, A Course of Higher Mathematics, Vol. 5, Fizmatgiz, Moscow (1960).Google Scholar

Copyright information

© Consultants Bureau, New York 1971

Authors and Affiliations

  • V. L. Oleinik
  • B. S. Pavlov

There are no affiliations available

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