Lars Hörmander defended his Ph.D. thesis at Lund University on 1955 October 22. His advisor, as first registered in the Mathematics Genealogy Project, was

Schwarz attended Weierstrass's lectures on Integral Calculus in 1861. Weierstrass was awarded an honorary doctorate by the University of Königsberg in 1854, so we cannot say he had a Ph.D. advisor. However, he studied mathematics for Gudermann in 1838—1840. In a more recent version of the Mathematics Genealogy Project, Gudermann is considered to be the advisor of Weierstrass, which makes it possible to go back to Gauss and Pfaff and even further...

Originally only Marcel Riesz was listed in the Mathematics Genealogy Project as an advisor of Lars Hörmander, and I had followed this link above. Later Lars Gĺrding (1919-03-07 — 2014-07-07) was introduced as a second advisor. In a publication Lars Hörmander wrote:

"When I defended my thesis in 1955 Lars Gĺrding was my advisor for Marcel Riesz had retired in 1953 and been in the US since then." (Hörmander 2003:61)

*Reference*

Hörmander, Lars. 2003. A tribute to Laurent
Schwartz. **In:** *Laurent Schwartz (1915—2002)*.
Supplément au numéro 98 de la Gazette des mathématiciens,
pp. 59–62. Paris: Société mathématique de France.

Christer Kiselman, 2015 March 17. To Kiselman's home page. E-mail address: kiselman@it.uu.se