The analysis of linear partial differential operators. II: Differential operators with constant coefficients.
Reprint of the 1983 edition.

*(English)*Zbl 1062.35004
Classics in Mathematics. Berlin: Springer (ISBN 3-540-22516-1/pbk). viii, 390 p. (2005).

This is a paperback edition of the 1990 edition of the second Volume of the author’s treatise on “The analysis of linear partial differential operators” (1990; Zbl 0687.35002). In the revised 1990 printing of Volume II, a number of minor flaws were corrected and the bibliography was updated and slightly enlarged. The paperback edition makes this volume more accessible.

Volume II is mainly devoted to partial differential operators with constant coefficients and convolution operators, with the exception of Chapter XIII which treats differential operators with constant strength. One of the main tools is Fourier Laplace transform We refer the reader to the excellent, detailed review [Grundlehren der Mathematischen Wissenschaften, 257. (Berlin Heidelberg-New York-Tokyo: Springer-Verlag) (1983; Zbl 0521.35002)].

The chapters in this volume, as the entire treatise, are excellently written, and make a rich, interesting and profitable reading. Since their publication these volumes have been a main reference for anyone working in the theory of linear partial different operators. Among many other authors, recent contributions on the theory of linear partial differential operators with constant coefficients and convolution operators on spaces of (ultra)distributions or spaces of real analytic functions have been obtained by C. Berenstein, R. Braun, P. Domanski, T. Gramchev, H. Komatsu, M. Langenbruch, R. Meise, A. Meril, N. Ortner, V. Palamodov, S. Pilipović, L. Rodino, D. C. Struppa, B. A. Taylor, D. Vogt and P. Wagner.

See the joint “Looking back”-review by Niels Jacob in Zbl 0712.35001.

Volume II is mainly devoted to partial differential operators with constant coefficients and convolution operators, with the exception of Chapter XIII which treats differential operators with constant strength. One of the main tools is Fourier Laplace transform We refer the reader to the excellent, detailed review [Grundlehren der Mathematischen Wissenschaften, 257. (Berlin Heidelberg-New York-Tokyo: Springer-Verlag) (1983; Zbl 0521.35002)].

The chapters in this volume, as the entire treatise, are excellently written, and make a rich, interesting and profitable reading. Since their publication these volumes have been a main reference for anyone working in the theory of linear partial different operators. Among many other authors, recent contributions on the theory of linear partial differential operators with constant coefficients and convolution operators on spaces of (ultra)distributions or spaces of real analytic functions have been obtained by C. Berenstein, R. Braun, P. Domanski, T. Gramchev, H. Komatsu, M. Langenbruch, R. Meise, A. Meril, N. Ortner, V. Palamodov, S. Pilipović, L. Rodino, D. C. Struppa, B. A. Taylor, D. Vogt and P. Wagner.

See the joint “Looking back”-review by Niels Jacob in Zbl 0712.35001.

Reviewer: José Bonet (Valencia)

##### MSC:

35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |

35Exx | Partial differential equations and systems of partial differential equations with constant coefficients |

42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |