On the solvability of pseudodifferential operators

Nils Dencker[1]

  • [1] Centre for Mathematical Sciences, University of Lund, Box 118, S-221 00 Lund, Sweden

Séminaire Équations aux dérivées partielles (2005-2006)

  • Volume: 43, Issue: 1, page 1-27

How to cite

top

Dencker, Nils. "On the solvability of pseudodifferential operators." Séminaire Équations aux dérivées partielles 43.1 (2005-2006): 1-27. <http://eudml.org/doc/11132>.

@article{Dencker2005-2006,
affiliation = {Centre for Mathematical Sciences, University of Lund, Box 118, S-221 00 Lund, Sweden},
author = {Dencker, Nils},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
number = {1},
pages = {1-27},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {On the solvability of pseudodifferential operators},
url = {http://eudml.org/doc/11132},
volume = {43},
year = {2005-2006},
}

TY - JOUR
AU - Dencker, Nils
TI - On the solvability of pseudodifferential operators
JO - Séminaire Équations aux dérivées partielles
PY - 2005-2006
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 43
IS - 1
SP - 1
EP - 27
LA - eng
UR - http://eudml.org/doc/11132
ER -

References

top
  1. Beals, R. and C. Fefferman, On local solvability of linear partial differential equations, Ann. of Math. 97 (1973), 482–498. Zbl0256.35002MR352746
  2. Bony, J.-M. and J.-Y. Chemin, Espaces fonctionnels associés au calcul de Weyl-Hörmander, Bull. Soc. Math. France 122 (1994), 77–118. Zbl0798.35172MR1259109
  3. Dencker, N., On the propagation of singularities for pseudo-differential operators of principal type, Ark. Mat. 20 (1982), 23–60. Zbl0503.58031MR660124
  4. —, The solvability of non L 2 solvable operators, Journées “Equations aux Dérivées Partielles” (Saint-Jean-de-Monts, 1996), Exp. No. X, 11 pp., Ecole Polytech., Palaiseau, 1996. Zbl0885.35151
  5. —, A sufficient condition for solvability, International Mathematics Research Notices 1999:12 (1999), 627–659. Zbl0947.58019MR1699215
  6. —, On the sufficiency of condition ( ψ ) , Report 2001:11, Centre for Mathematical Sciences, Lund University. 
  7. —, The solvability of pseudo-differential operators, Phase space analysis of partial differential equations, Vol. I, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, 2004, 175–200. Zbl1079.35105MR2144409
  8. —, The resolution of the Nirenberg-Treves conjecture, Ann. of Math. 163 (2006), 405–444. Zbl1104.35080MR2199222
  9. Hörmander, L., The Weyl calculus of pseudo-differential operators, Comm. Pure Appl. Math. 32 (1979), 359–443. Zbl0388.47032MR517939
  10. —, Pseudo-differential operators of principal type, Singularities in boundary value problems (Proc. NATO Adv. Study Inst., Maratea, 1980) NATO Adv. Study Inst. Ser. C: Math. Phys. Sci., 65, Reidel, Dordrecht-Boston, Mass., 1981, 69–96. Zbl0459.35096
  11. —, The analysis of linear partial differential operators, vol. I–IV, Springer Verlag, Berlin, 1983–1985. Zbl1124.05078
  12. —, Notions of convexity, Birkhäuser, Boston, 1994. Zbl0835.32001MR1301332
  13. —, On the solvability of pseudodifferential equations, Structure of solutions of differential equations (M. Morimoto and T. Kawai, eds.), World Scientific, New Jersey, 1996, 183–213. Zbl0897.35082MR1445329
  14. —, The proof of the Nirenberg–Treves conjecture according to N. Dencker och N. Lerner, Preprint. 
  15. Lerner, N., Sufficiency of condition ( ψ ) for local solvability in two dimensions, Ann. of Math. 128 (1988), 243–258. Zbl0682.35112MR960946
  16. —, Nonsolvability in L 2 for a first order operator satisfying condition ( ψ ) , Ann. of Math. 139 (1994), 363–393. Zbl0818.35152MR1274095
  17. —, Energy methods via coherent states and advanced pseudo-differential calculus, Multidimensional complex analysis and partial differential equations (P. D. Cordaro, H. Jacobowitz, and S. Gidikin, eds.), Amer. Math. Soc., Providence, R.I., USA, 1997, 177–201. Zbl0885.35152MR1447224
  18. —, Perturbation and energy estimates, Ann. Sci. École Norm. Sup. 31 (1998), 843–886. Zbl0927.35139MR1664214
  19. —, The Wick calculus of pseudo-differential operators and some of its applications. Cubo Mat. Educ. 5 (2003), 213–236. Zbl05508173MR1957713
  20. —, Cutting the loss of derivatives for solvability under condition ( Ψ ), Preprint. Zbl1181.35355
  21. Lewy, H. An example of a smooth linear partial differential equation without solution, Ann. of Math. 66 (1957), 155–158. Zbl0078.08104MR88629
  22. Moyer, R.D., Local solvability in two dimensions: Necessary conditions for the principal-type case, Mimeographed manuscript, University of Kansas, 1978. 
  23. Nirenberg, L. and F. Treves, On local solvability of linear partial differential equations. Part I: Necessary conditions, Comm. Pure Appl. Math. 23 (1970), 1–38, Part II: Sufficient conditions, Comm. Pure Appl. Math. 23 (1970), 459–509; Correction, Comm. Pure Appl. Math. 24 (1971), 279–288. Zbl0191.39103
  24. Trépreau, J.M., Sur la résolubilité analytique microlocale des opérateurs pseudodifférentiels de type principal, Ph.D. thesis, Université de Reims, 1984. Zbl0489.35082

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.