# Regularity Properties of Oscillatory Integral Operators - DiVA

Kalender SMC

One of them in the second half of the XXth century was Lars Valter H ormander (24 January 1931 { 25 November 2012) In mathematics, Hörmander's condition is a property of vector fields that, if satisfied, has many useful consequences in the theory of partial and stochastic differential equations.The condition is named after the Swedish mathematician Lars Hörmander I have a question on the introduction to Hormanders first PDE book. The introduction seems poorly (i.e. confusingly) written to me, hopefully the rest of the book is better. Anyway, he says classical solutions of the wave equation $$\frac{\partial^2}{\partial x^2}v - \frac{\partial^2}{\partial y^2}v = 0,$$ are twice continuously differentiable functions satisfying the equation everywhere.

Review by: L Cattabriga. So, we have Hormander's book. Lars Hormander is known for writing high-level math texts (both in quality and difficulty), as seen in his famous 4-volume series about PDE's, and this book is no exception. Contents 1 A primer on C1 0-functions 6 2 De nition of distributions 11 3 Operations on distributions 17 4 Finite parts 21 5 Fundamental solutions of the Laplace and heat equations 28 Se hela listan på ncatlab.org By a theorem of Hormander [6], if Xx, .

Opening ceremony of ICM in Stockholm, 1962.

## Partiella differentialekvationer med distributionsteori 2003-2004

Sobolev S. 1989, Partial Differential Equations of Mathematical Physics, Dover, New York. But from what I can understand, the main theorem 1.1 (usually referred to as "Hörmander's Theorem") says (roughly) that if a second order differential operator P satisfies some conditions then it is hypoelliptic. Which in turn means that if P u is smooth, then u must be smooth.

### Kaj Nyström - Uppsala University, Sweden

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Lars Hormander is known for writing high-level math texts (both in quality and difficulty), as seen in his famous 4-volume series about PDE's, and this book is no exception.

[11] A. Calderon and R. Vaillancourt, On the boundedness of pseudo-diﬀerential operators, J. … An introduction to Gevrey Spaces. Fernando de Ávila Silva Federal University of Paraná - Brazil Seminars on PDE’s and Analysis (UFPR-BRAZIL) April 2017 - Curitiba 1 / 25 Even there, there is a distinction between elliptic, hypo-elliptic and hyperbolic PDE's read carefully the question : it not only about linear PDEs, which is the case in the book of Hormander Lars Hormander is known for writing high-level math texts (both in quality and difficulty), as seen in his famous 4-volume series about PDE's, and this book is no exception.

Lars Hormander is known for writing high-level math texts (both in quality and difficulty), as seen in his famous 4-volume series about PDE's, and this book is no exception. The two volumes which are out, and their companions which will follow, will not likely serve as the texts for one's first brush with PDE, but the serious analyst will find here an elegant presentation of a vast amount of material on linear PDE, by a consummate master of the subject.
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