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Book DetailsContemporary MathematicsVolume: 368; 2005; 414 ppMSC: Primary 35; 32
This volume is dedicated to François Treves, who made substantial contributions to the geometric side of the theory of partial differential equations (PDEs) and several complex variables. One of his best-known contributions, reflected in many of the articles here, is the study of hypo-analytic structures.
An international group of well-known mathematicians contributed to the volume. Articles generally reflect the interaction of geometry and analysis that is typical of Treves's work, such as the study of the special types of partial differential equations that arise in conjunction with CR-manifolds, symplectic geometry, or special families of vector fields. There are many topics in analysis and PDEs covered here, unified by their connections to geometry.
The material is suitable for graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.
ReadershipGraduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.
-
Table of Contents
-
Articles
-
Patrick Ahern and Xianghong Gong — Cusp-type singularities of real analytic curves in the complex plane [ MR 2126461 ]
-
S. Berhanu and J. Hounie — The F. and M. Riesz property for vector fields [ MR 2126462 ]
-
Antonio Bove — Gevrey hypo-ellipticity for sums of squares of vector fields: some examples [ MR 2126463 ]
-
Haïm Brezis, Petru Mironescu and Augusto C. Ponce — $W^{1,1}$-maps with values into $S^1$ [ MR 2126464 ]
-
Sagun Chanillo — Analytic hypoellipticity and spectral problems for Schrödinger’s equation [ MR 2126465 ]
-
Hua Chen and Zhuangchu Luo — Formal solutions for higher order nonlinear totally characteristic PDEs with irregular singularities [ MR 2126466 ]
-
Ferruccio Colombini and Nicolas Lerner — Uniqueness of $L^\infty $ solutions for a class of conormal $BV$ vector fields [ MR 2126467 ]
-
Paulo D. Cordaro and Nicholas Hanges — Impact of lower order terms on a model PDE in two variables [ MR 2126468 ]
-
Makhlouf Derridj and David S. Tartakoff — Global analytic hypoellipticity for a class of quasilinear sums of squares of vector fields [ MR 2126469 ]
-
Michael Eastwood — Representations via overdetermined systems [ MR 2126470 ]
-
Gábor Francsics and Peter D. Lax — A semi-explicit fundamental domain for a Picard modular group in complex hyperbolic space [ MR 2126471 ]
-
Simon Gindikin — Complex horospherical transform on real sphere [ MR 2126472 ]
-
Jennifer Gorsky and A. Alexandrou Himonas — On analyticity in space variable of solutions to the KdV equation [ MR 2126473 ]
-
Lars Hörmander — The multinomial distribution and some Bergman kernels [ MR 2126474 ]
-
Xiaojun Huang, Shanyu Ji and Dekang Xu — Several results for holomorphic mappings from $\mathbf {B}^n$ into $\mathbf {B}^N$ [ MR 2126475 ]
-
Howard Jacobowitz — Whitney and Mizohata structures [ MR 2126476 ]
-
Alessia Elisabetta Kogoj and Ermanno Lanconelli — One-side Liouville theorems for a class of hypoelliptic ultraparabolic equations [ MR 2126477 ]
-
László Lempert — Acyclic sheaves in Banach spaces [ MR 2126478 ]
-
Aobing Li and Yan Yan Li — A Liouville type theorem for some conformally invariant fully nonlinear equations [ MR 2126479 ]
-
Severino T. Melo — Norm closure of classical pseudodifferential operators does not contain Hörmander’s class [ MR 2126480 ]
-
Guy Métivier — Remarks on the well-posedness of the nonlinear Cauchy problem [ MR 2127041 ]
-
Abdelhamid Meziani — Representation of solutions of planar elliptic vector fields with degeneracies [ MR 2127042 ]
-
Louis Nirenberg — Some recollections of working with François Treves [ MR 2127043 ]
-
Mei-Chi Shaw — Boundary value problems on Lipschitz domains in $\Bbb R^n$ or $\Bbb C^n$ [ MR 2127044 ]
-
Sergio Spagnolo — Hyperbolic systems well posed in all Gevrey classes [ MR 2127045 ]
-
-
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This volume is dedicated to François Treves, who made substantial contributions to the geometric side of the theory of partial differential equations (PDEs) and several complex variables. One of his best-known contributions, reflected in many of the articles here, is the study of hypo-analytic structures.
An international group of well-known mathematicians contributed to the volume. Articles generally reflect the interaction of geometry and analysis that is typical of Treves's work, such as the study of the special types of partial differential equations that arise in conjunction with CR-manifolds, symplectic geometry, or special families of vector fields. There are many topics in analysis and PDEs covered here, unified by their connections to geometry.
The material is suitable for graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.
Graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.
-
Articles
-
Patrick Ahern and Xianghong Gong — Cusp-type singularities of real analytic curves in the complex plane [ MR 2126461 ]
-
S. Berhanu and J. Hounie — The F. and M. Riesz property for vector fields [ MR 2126462 ]
-
Antonio Bove — Gevrey hypo-ellipticity for sums of squares of vector fields: some examples [ MR 2126463 ]
-
Haïm Brezis, Petru Mironescu and Augusto C. Ponce — $W^{1,1}$-maps with values into $S^1$ [ MR 2126464 ]
-
Sagun Chanillo — Analytic hypoellipticity and spectral problems for Schrödinger’s equation [ MR 2126465 ]
-
Hua Chen and Zhuangchu Luo — Formal solutions for higher order nonlinear totally characteristic PDEs with irregular singularities [ MR 2126466 ]
-
Ferruccio Colombini and Nicolas Lerner — Uniqueness of $L^\infty $ solutions for a class of conormal $BV$ vector fields [ MR 2126467 ]
-
Paulo D. Cordaro and Nicholas Hanges — Impact of lower order terms on a model PDE in two variables [ MR 2126468 ]
-
Makhlouf Derridj and David S. Tartakoff — Global analytic hypoellipticity for a class of quasilinear sums of squares of vector fields [ MR 2126469 ]
-
Michael Eastwood — Representations via overdetermined systems [ MR 2126470 ]
-
Gábor Francsics and Peter D. Lax — A semi-explicit fundamental domain for a Picard modular group in complex hyperbolic space [ MR 2126471 ]
-
Simon Gindikin — Complex horospherical transform on real sphere [ MR 2126472 ]
-
Jennifer Gorsky and A. Alexandrou Himonas — On analyticity in space variable of solutions to the KdV equation [ MR 2126473 ]
-
Lars Hörmander — The multinomial distribution and some Bergman kernels [ MR 2126474 ]
-
Xiaojun Huang, Shanyu Ji and Dekang Xu — Several results for holomorphic mappings from $\mathbf {B}^n$ into $\mathbf {B}^N$ [ MR 2126475 ]
-
Howard Jacobowitz — Whitney and Mizohata structures [ MR 2126476 ]
-
Alessia Elisabetta Kogoj and Ermanno Lanconelli — One-side Liouville theorems for a class of hypoelliptic ultraparabolic equations [ MR 2126477 ]
-
László Lempert — Acyclic sheaves in Banach spaces [ MR 2126478 ]
-
Aobing Li and Yan Yan Li — A Liouville type theorem for some conformally invariant fully nonlinear equations [ MR 2126479 ]
-
Severino T. Melo — Norm closure of classical pseudodifferential operators does not contain Hörmander’s class [ MR 2126480 ]
-
Guy Métivier — Remarks on the well-posedness of the nonlinear Cauchy problem [ MR 2127041 ]
-
Abdelhamid Meziani — Representation of solutions of planar elliptic vector fields with degeneracies [ MR 2127042 ]
-
Louis Nirenberg — Some recollections of working with François Treves [ MR 2127043 ]
-
Mei-Chi Shaw — Boundary value problems on Lipschitz domains in $\Bbb R^n$ or $\Bbb C^n$ [ MR 2127044 ]
-
Sergio Spagnolo — Hyperbolic systems well posed in all Gevrey classes [ MR 2127045 ]
