Correspondence of Marcel Riesz with Swedes. Part II. file: Riesz1.tex

0.17. FOLKE ODQVIST 49
skolpojkarna smäller ryska smällare för dig, samt om det gängse akademiska
skvallret. Min vördnad till dina föräldrar. Hälsa Ekman gott nytt år!
Tillgivne Folke X.
Translation:
Dear brother Håkan, Exiled in the country of the barbarians, I write to you in a
purely egoistic purpose. Namely, in the investigation of a 2-dimension/al hydrodynamical
problem for a viscous fluid I was led to the following problem: Find the sequence of
continuation functions that map (see Figur ) the domain (2) between the circle C and
the real axis onto the halfplane X and haves a singularity of order n i z = infinity.
The simple case when the singularity is a branching point, apparently, can be treated with
but for n ≥ 1 one gets X of the form
X =
X = log z − iα
z + iα
a −n
(z − ia) n + · · · + a −1
z − ia + a 0 + a 1 (z − ia) + . . .
Next one asks. Has anybody treated this system of functions 32 If you do not know it
yourself ask Riesz or Carleman or another reliable person!
I work at full speed with experiments which yp to now have beem successful. I add a
copiw where the dashed portion is precisely the vortex domain predicte in my licentiate
thesis.
Moreover, I have been corresponding with Oséen 33 , who apparently has approved as
a theme for thesis: Mutual influence between heat conductiong and liquid flow. It is an
application of the method of Lamb with “solid harmonics” in a special (experimentally
treated by Burgers) that led me to the issue mentioned.
32 As you see immediately, one gets X = (z + 1 z )n if the straight boundary/ line is allow
to stretch out to infinity and the coordinate system is moved in a suitable manner.
33 Oséen, Carl Wilhelm, 1879-1944, professor of mechanics and mathematical physicc
since 1909 at UU, one of the founders of the Swedish Society of Physicists and its first
Chairman. O’s in part pioneering activities covered hydromechanics, electromagnetism
and optics, for example the Ewald-Oseen extinction theorem, describing the refraction of
light at the limit surface for a rigid body as a diffusion phenomenon. O. explained further
the d’Alembert paradox, that is that resistance of liquids of low viscosity theoretically was
negligible, in contrast to the experimental experiece. O. was one of the first to present a
theoretical explanation of the behaviour of floating crystals. [114].