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Uspekhi Mat. Nauk, 1971, Volume 26, Issue 1(157), Pages 67–112 (Mi umn5166)  

This article is cited in 27 scientific papers (total in 27 papers)

The stationary phase method and pseudodifferential operators

M. V. Fedoryuk

Abstract: In the paper asymptotic expansions are calculated for integrals
$$ \int f(x)\exp(i\lambda g(x))dx,\qquad\lambda\to+\infty, $$
of rapidly oscillating functions, in which $x\in R^n$, $f$ and $g$ are smooth functions, and $g$ is real-valued. The results obtained serve to develop a calculus of pseudodifferential operators and generalizations of them, the Fourier integral operators.

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English version:
Russian Mathematical Surveys, 1971, 6:1, 65–115

Bibliographic databases:

UDC: 517.43
MSC: 47G30, 58J40, 41A60, 35S30
Received: 11.06.1970

Citation: M. V. Fedoryuk, “The stationary phase method and pseudodifferential operators”, Uspekhi Mat. Nauk, 26:1(157) (1971), 67–112; Russian Math. Surveys, 6:1 (1971), 65–115

Citation in format AMSBIB
\by M.~V.~Fedoryuk
\paper The stationary phase method and pseudodifferential operators
\jour Uspekhi Mat. Nauk
\yr 1971
\vol 26
\issue 1(157)
\pages 67--112
\jour Russian Math. Surveys
\yr 1971
\vol 6
\issue 1
\pages 65--115

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    2. V. V. Kucherenko, “Asymptotics of the solution of the system $A(x,-ih\frac\partial{\partial x})$ as $h\to0$ in the case of characteristics of variable multiplicity”, Math. USSR-Izv., 8:3 (1974), 631–666  mathnet  crossref  mathscinet  zmath
    3. Yu. V. Egorov, “Subelliptic operators”, Russian Math. Surveys, 30:2 (1975), 59–118  mathnet  crossref  mathscinet  zmath
    4. M. V. Fedoryuk, “Of Fourier integral operators and the asymptotic behaviour of the solution of the mixed problem”, Russian Math. Surveys, 32:6 (1977), 67–120  mathnet  crossref  mathscinet  zmath
    5. M. V. Karasev, V. E. Nazaikinskii, “On the quantization of rapidly oscillating symbols”, Math. USSR-Sb., 34:6 (1978), 737–764  mathnet  crossref  mathscinet  zmath
    6. Daisuke Fujiwara, “A construction of the fundamental solution for the Schrödinger equation”, J Anal Math, 35:1 (1979), 41  crossref  mathscinet  zmath  isi
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    14. R. A. Corns, T. A. Osborn, “Propagators for relativistic systems with non-Abelian interactions”, J Math Phys (N Y ), 31:4 (1990), 901  crossref  mathscinet  zmath  adsnasa  isi
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