Mathematical Analysis

1. Front Matter

   Pages i-viii

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2. Systems of Linear Differential Equations

   • V. P. Palamodov

   Pages 1-35

3. Fredholm Operators and Their Generalizations

   • S. N. Krachkovskii, A. S. Dikanskii

   Pages 37-72

4. Representations of Groups and Algebras in Spaces with Indefinite Metric

   • M. A. Naimark, R. S. Ismagilov

   Pages 73-109

The present book contains three articles: "Systems of Linear Differential Equations," by V. P. Palamodov; "Fredholm Operators and Their Generalizations," by S. N. Krachkovskii and A. S. Di­ kanskii; and "Representations of Groups and Algebras in Spaces with an Indefinite Metric" by M. A. Naimark and R. S. Ismagilov. In the fi.rst article the accent is on those characteristics of systems of differential equations which distinguish the systems from the scalar case. Considerable space is devoted in particular to "nonquadratic systems," a topic that has very recently stimulated interest. The second article is devoted to the algebraic aspects of the theory of operators (determinant theory in particular) in Banach and linear topological spaces. The third article reflects the present state of the art in the given area of the theory of representations, which has been re­ ceiving considerable attention in connection with its applications in physics (particularly in quantum field theory) and in the theory of differential equations.

• algebra
• calculus
• differential equation
• equation
• Mathematica
• mathematical analysis

• V.A. Steklov Mathematics Institute, Academy of Sciences of the USSR, Moscow, USSR

  R. V. Gamkrelidze

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