# College of Arts & SciencesDepartment of Mathematics

## Manfred Stoll

#### Distinguished Professor Emeritus Department of Mathematics University of South Carolina

 Phone Number: Email: stoll@math.sc.edu Office: LeConte 309D Curriculum vitae: Download PDF

#### Background

Publications of Manfred Stoll

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1. MR1936731 Stoll, Manfred Harmonic majorants for eigenfunctions of the Laplacian with finite Dirichlet integrals. J. Math. Anal. Appl. 274 (2002), no. 2, 788--811.
2. MR1885760 Stoll, Manfred On the integrability of eigenfunctions of the Laplace-Beltrami operator in the unit ball of $\Bbb C\sp n$. Potential Anal. 16 (2002), no. 3, 205--220.
3. MR1849990 Stoll, Manfred Holomorphic and $\scr M$-harmonic functions with finite Dirichlet integral on the unit ball of ${\Bbb C}\sp n$. Illinois J. Math. 45 (2001), no. 1, 139--162.
4. MR1673942 Stoll, Manfred Weighted tangential boundary limits of subharmonic functions on domains in $R\sp n (n\geq2)$. Math. Scand. 83 (1998), no. 2, 300--308.
5. MR1407502 Stoll, Manfred Boundary limits and non-integrability of $\scr M$-subharmonic functions in the unit ball of $\bold C\sp n$ $(n\geq 1)$. Trans. Amer. Math. Soc. 349 (1997), no. 9, 3773--3785.
6. MR1700265 Hahn, K. T.; Stoll, M.; Youssfi, E. H. Invariant potentials and tangential boundary behavior of $\scr M$-subharmonic functions in the unit ball. Complex Variables Theory Appl. 28 (1995), no. 1, 67--96.
7. MR1323823 Stoll, Manfred Non-isotropic Hausdorff capacity of exceptional sets of invariant potentials. Potential Anal. 4 (1995), no. 2, 141--155.
8. MR1297545 Stoll, Manfred Invariant potential theory in the unit ball of $C\sp n$. London Mathematical Society Lecture Note Series, 199. Cambridge University Press, Cambridge, 1994. x+173 pp. ISBN: 0-521-46830-2
9. MR1231501 Stoll, Manfred Tangential boundary limits of invariant potentials in the unit ball of $C\sp n$. J. Math. Anal. Appl. 177 (1993), no. 2, 553--571.
10. MR1223898 Stoll, Manfred A characterization of Hardy spaces on the unit ball of $C\sp n$. J. London Math. Soc. (2) 48 (1993), no. 1, 126--136.
11. MR1124151 Stoll, Manfred A characterization of Hardy-Orlicz spaces on planar domains. Proc. Amer. Math. Soc. 117 (1993), no. 4, 1031--1038.
12. MR1216108 Stoll, Manfred Composition of potentials with inner functions. Math. Scand. 71 (1992), no. 1, 122--132.
13. MR1157925 Stoll, Manfred Admissible limits of invariant potentials in the unit ball of $C\sp n$. Complex Variables Theory Appl. 18 (1992), no. 3-4, 167--185.
14. MR1155728 Stoll, M. Rate of growth of $p$th means of invariant potentials in the unit ball of $C\sp n$. II. J. Math. Anal. Appl. 165 (1992), no. 2, 374--398.
15. MR1147053 Liu, S. H.; Stoll, M. Projections on spaces of holomorphic functions on certain domains in $C\sp 2$. Complex Variables Theory Appl. 17 (1992), no. 3-4, 223--233.
16. MR1082003 Stoll, M. Uniform limits of Green potentials in the unit disc. Arch. Math. (Basel) 56 (1991), no. 1, 58--67.
17. MR1022549 Stoll, M. Rate of growth of $p$th means of invariant potentials in the unit ball of $C\sp n$. J. Math. Anal. Appl. 143 (1989), no. 2, 480--499.
18. MR0936479 Hahn, K. T.; Stoll, M. Boundary limits of Green potentials on the ball in $C\sp n$. Complex Variables Theory Appl. 9 (1988), no. 4, 359--371.
19. MR0870281 Bennett, Colin; Stoll, Manfred Derivatives of analytic functions and bounded mean oscillation. Arch. Math. (Basel) 47 (1986), no. 5, 438--442.
20. MR0802292 Stoll, Manfred Mean growth and Fourier coefficients of some classes of holomorphic functions on bounded symmetric domains. Ann. Polon. Math. 45 (1985), no. 2, 161--183.
21. MR0792369 Stoll, Manfred Boundary limits of Green potentials in the unit disc. Arch. Math. (Basel) 44 (1985), no. 5, 451--455.
22. MR0774024 Stoll, M. Boundary limits of subharmonic functions in the disc. Proc. Amer. Math. Soc. 93 (1985), no. 3, 567--568.
23. MR0709577 Nestlerode, W. C.; Stoll, M. Radial limits of $n$-subharmonic functions in the polydisc. Trans. Amer. Math. Soc. 279 (1983), no. 2, 691--703.
24. MR0699704 Stoll, Manfred On the rate of growth of the means $M\sb{p}$ of holomorphic and pluriharmonic functions on the ball. J. Math. Anal. Appl. 93 (1983), no. 1, 109--127.
25. MR0599247 Stoll, Manfred Radial limits of the Poisson kernel on the classical Cartan domains. Ann. Polon. Math. 38 (1980), no. 2, 207--216.
26. MR0526616 Stoll, Manfred Invertible and weakly invertible singular inner functions in the Bergman spaces. Arch. Math. (Basel) 31 (1978/79), no. 5, 501--508.
27. MR0492324 Roberts, James W.; Stoll, Manfred Correction to the paper: "Prime and principal ideals in the algebra $N\sp{+}$" (Arch. Math. (Basel) 27 (1976), 387--393). Arch. Math. (Basel) 30 (1978), no. 6, 672.
28. MR0463920 Stoll, M. Mean growth and Taylor coefficients of some topological algebras of analytic functions. Ann. Polon. Math. 35 (1977/78), no. 2, 139--158.
29. MR0437812 Stoll, M. Mean value theorems for harmonic and holomorphic functions on bounded symmetric domains. J. Reine Angew. Math. 290 (1977), 191--198.
30. MR0435817 Roberts, James W.; Stoll, Manfred Composition operators on $F\sp{+}$. Studia Math. 57 (1976), no. 3, 217--228.
31. MR0422639 Roberts, James W.; Stoll, Manfred Prime and principal ideals in the algebra $N\sp{+}$. Arch. Math. (Basel) 27 (1976), no. 4, 387--393.
32. MR0417438 Stoll, Manfred The space $N\sb*$ of holomorphic functions on bounded symmetric domains. Ann. Polon. Math. 32 (1976), no. 1, 95--110.
33. MR0404692 Stoll, Manfred Harmonic majorants for plurisubharmonic functions on bounded symmetric domains with applications to the spaces $H\sb{F}$ and $N\sb{\sp*}$. J. Reine Angew. Math. 282 (1976), 80--87.
34. MR0399471 Stoll, M. A characterization of $F\sp{+}\cap N$. Proc. Amer. Math. Soc. 57 (1976), no. 1, 97--98.
35. MR0372221 Stoll, M. Properties of the space $\tilde h\sp{p}$ $(0<p\leq 1)$ of harmonic functions on the unit disc. Arch. Math. (Basel) 25 (1974), 613--618.
36. MR0364691 Stoll, Manfred Hardy-type spaces of harmonic functions on symmetric spaces of noncompact type. J. Reine Angew. Math. 271 (1974), 63--76.
37. MR0338448 Stoll, M. Integral formulae for pluriharmonic functions on bounded symmetric domains. Duke Math. J. 41 (1974), 393--404.

#### Research

Potential Theory, Several Complex Variables. Research interests include: the study of holomorphic, harmonic, and plurisubharmonic functions of one and several complex variables; Hpspaces, Bergmann spaces, and other spaces of harmonic and holomorphic functions of one and several complex variables; boundary behavior of Green potentials in domains in Rn and Cn.

#### Teaching

Lecture Notes and Preprints:

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