The Analysis of Linear Partial Differential Operators III

By L. Hörmander. 2007

1,809 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/78fdb07317db95f1a17d6a239efa114a6293b998

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Gunther Uhlmann
2. Mikko Salo
3. Carlos E. Kenig
4. Michael Ruzhansky
5. David dos Santos Ferreira
6. Matti Lassas
7. Ziemowit Rzeszotnik
8. F. Merle

In Computational Theory and Mathematics

1. Mikko Salo
2. Gunther Uhlmann
3. Matti Lassas
4. Carlos E. Kenig
5. David dos Santos Ferreira
6. Yaroslav Kurylev
7. G. Eskin
8. Michael Ruzhansky

In Mathematical Physics

1. Mikko Salo
2. Gunther Uhlmann
3. Carlos E. Kenig
4. David dos Santos Ferreira
5. Matti Lassas
6. Yaroslav Kurylev
7. Michael Ruzhansky
8. F. Merle

Citations in the corpus

• The orbit method and analysis of automorphic forms (2018, result): “Although we have been unable to find a reference containing similar results, we regard most of the contents of Part I as philosophically unsurprising generalizations of standard results in the theory of pseudodifferential operators (see [42, 5] and references), which corresponds roughly to the case ”
• Inverse Hyperbolic Problems with Time-Dependent Coefficients (2005, methodology): “Denote by w1p p = 1 2 the unique solution of L1w1p = g1p for t > T1 such that w1p = 0 for t > T (c.f. Hormander, 1985).”
• The stability for the Cauchy problem for elliptic equations (2009, background): “With no ambition of completeness, let us mention Hörmander [44], Jerison and Kenig [50], Garofalo and Lin [32, 33], Fabes, Garofalo and Lin [30] and, more recently, Koch and Tataru [55].”
• Limiting Carleman weights and anisotropic inverse problems (2008, background): “We denote by p ∼ ∑ pj the asymptotic sum of symbols, see [10] for these basic facts.”
• Unique continuation and decay for the Korteweg-de Vries equation with localized damping (2005, background): “We point out that such inequalities are those reminiscent of the classical Carleman estimates in which the lower order terms (with bounded coefficients or even with unbounded coefficients under suitable integrability conditions) of the equation can be controlled in some weighted norms by the princip”
• Inverse problems: seeing the unseen (2014, result): “Using the watermelon approach [105,174], one then shows that there is an exponential decay of this transform for other directions implying that the point (x0, ν), where ν is the normal to the point x0, is not in the analytic wave front set of f in contradiction to the microlocal version of Holmgren’”
• Time quasi-periodic gravity water waves in finite depth (2017, methodology): “We now prove the existence of a solution of equation (8.8) by means of the Nash-Moser-Hörmander theorem proved in [10], whose statement is given in Appendix B.”
• Banach algebras of pseudodifferential operators and their almost diagonalization (2007, positive): “On the one hand we have rA(δλ) = lim n→∞ ‖δnλ‖ 1/n A = limn→∞ ‖δnλ‖ 1/n A = limn→∞ω(nλ) 1/n .”