Bulletin of the American Mathematical Society

Author(s): Lipman Bers
Journal: Bull. Amer. Math. Soc. 62 (1956), 291-331.
MathSciNet review: 0081936
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1.: S. Agmon and L. Bers, The expansion theorem for pseudoanalytic functions, Proc. Amer. Math. Soc. vol. 3 (1952) pp. 757-764. MR 57349
2.: L. Ahlfors, On quasi-conformal mappings, Journal d'Analyse Mathématique vol. 4 (1954) pp. 1-58.
3.: E. Beltrami, Sulle funzioni potenziali di sistemi simmetrici intorno ad un asse, Opere matematice, Vol. 3, Milano, 1911, pp. 115-128.
4.: E. Beltrami, Sulle teoria delle funzioni potenziali simmetriche, ibid., pp. 349-377.
5.: P. W. Berg, On the existence of Helmholtz flows of a compressible fluid, Dissertation, New York University, 1953.
6.: S. Bergman, Functions satisfying certain partial differential equations of elliptic type and their representation, Duke Math. J. vol. 14 (1947) pp. 349-366. MR 22262
7.: S. Bergman, Linear operators in the theory of partial differential equations, Trans. Amer. Math. Soc. vol. 53 (1943) pp. 130-155. MR 7555
8.: S. Bergman, A formula for the streamfunction of certain flows, Proc. Nat. Acad. Sci. U. S. A. vol. 29 (1943) pp. 276-281. MR 10079
9.: L. Bers, The expansion theorem for sigma-monogenic functions, Amer. J. Math. vol. 72 (1950) pp. 705-712. MR 44005
10.: L. Bers, On the continuation of a potential gas flow across the sonic line, N.A.C.A. Technical Note No. 2058, 1950. MR 36121
11.: L. Bers, Partial differential equations and generalized analytic functions, Proc. Nat. Acad. Sci. U.S.A. vol. 36, (1950) pp. 130-136; Second note, ibid., vol. 37 (1951) pp. 42-47. MR 44006
12.: L. Bers, Theory of pseudo-analytic functions, Lecture notes (mimeographed), New York University, 1953. MR 57347
13.: L. Bers, Univalent solutions of linear elliptic systems, Comm. Pure Appl. Math. vol. 6 (1953) pp. 513-526. MR 58830
14.: L. Bers, Nonlinear elliptic equations without nonlinear entire solutions, Journal of Rational Mechanics and Analysis vol. 3 (1954) pp. 767-787. MR 67313
15.: L. Bers, Function-theoretical properties of solutions of partial differential equations of elliptic type, Annals of Mathematics Studies, no. 33, 1954, pp. 69-94. MR 70009
16.: L. Bers, Existence and uniqueness of a subsonic flow past a given profile, Comm. Pure Appl. Math. vol. 7 no. 3 (1954) pp. 441-504. MR 65334
17.: L. Bers, Local behavior of solutions of general linear elliptic equations, Comm. Pure Appl. Math. vol. 8, no. 4 (1955). MR 75416
18.: L. Bers, Local theory of pseudoanalytic functions, Lectures on functions of a complex variable, Michigan University Press, 1955, pp. 213-244. MR 76043
19.: L. Bers, Remark on an application of pseudoanalytic functions, Amer. J. Math. vol. 78 (1956) pp. 486-496. MR 87000
20.: L. Bers, Partial differential equations and pseudoanalytic functions on Riemann surfaces, Annals of Mathematics Studies, no. 30, 1953, pp. 157-165. MR 57990
21.: L. Bers and A. Gelbart, On a class of differential equations in mechanics of continua, Quarterly of Applied Mathematics vol. 1 (1943) pp. 168-188. MR 8556
22.: L. Bers and A. Gelbart, On a class of functions defined by partial differential equations, Trans. Amer. Math. Soc. vol. 56 (1944) pp. 67-93. MR 10910
23.: L. Bers and A. Gelbart, On generalized Laplace transformations, Ann. of Math. vol. 48 (1947) pp. 342-357. MR 20152
24.: L. Bers, and L. Nirenberg, On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications, Convegno Internazionale sulle Equazioni Derivate e Parziali, Agosto, 1954, pp. 111-140. MR 76981
25.: L. Bers, and L. Nirenberg, On linear and nonlinear elliptic boundary value problems in the plane, Convegno Internazionale sulle Equazioni Derivate e Parziali, Agosto, 1954, pp. 141-167. MR 76982
26.: W. M. Boothby, The topology of the level curves of harmonic functions with critical points, Amer. J. Math. vol. 73 no. 3 (1951) pp. 512-538. MR 43456
27.: R. Cacciopoli, Fondamenti per una teoria generale delle funzioni pseudoanalitiche di una variabile complessa, Academia nazionale dei Lincei, Rendiconti vol. 13 (1952) pp. 197-204 and 321-329. MR 56718
28.: T. Carleman, Sur les systèmes linéaires aux dérivées partielles du premier ordre à deux variables, C. R. Acad. Sci. Paris vol. 197 (1933) pp. 471-474.
29.: T. Carleman, Sur un problème d'unicité pour les systèmes d'équations aux dérivées partielles à deux variables indépendentes, Arkiv för Matematik, Astronomi och Fysik vol. 26B No. 17 (1939) pp. 1-9.
30.: H. H. Chang, Approximately analytic functions of bounded type and boundary behavior of solutions of elliptic partial differential equations, Acta Math. Sinica vol. 3 (1953) pp. 101-132. MR 71548
31.: J. B. Diaz, On a class of partial differential equations of even order, Amer. J. Math. vol. 68 (1946) pp. 611-659. MR 19828
32.: A. Douglis, A function-theoretic approach to elliptic systems of equations in two variables, Comm. Pure Appl. Math. vol. 6 (1953) pp. 259-289. MR 64277
33.: A. Douglis, Uniqueness in Cauchy problems for elliptic systems of equations, Comm. Pure Appl. Math. vol. 6 (1953) pp. 291-298. MR 64278
34.: A. Douglis, Function-theoretic properties of certain elliptic systems of first order equations, Lectures on Functions of a Complex Variable, Michigan University Press, 1953, pp. 335-340. MR 70829
35.: A. Gelbart, On a function-theory method for obtaining potential flow patterns of a compressible fluid, N.A.C.A. ARR No. 3G27, 1943.
36.: J. J. Gergen and F. G. Dressel, Mapping by p-regular functions, Duke Math. J. vol. 18 no. 1 (1951) pp. 185-210. MR 50019
37.: J. J. Gergen and F. G. Dressel, Mapping for elliptic equations, Trans. Amer. Math. Soc. vol. 77 (1954) pp. 151-178. MR 63533
38.: J. J. Gergen and F. G. Dressel, Uniqueness for p-regular mapping, Duke Math. J. vol. 19 (1952) pp. 435-444. MR 50020
39.: P. Hartman and A. Wintner, On the third fundamental form of a surface, Amer. J. Math. vol. 75 (1953) pp. 298-334. MR 55734
40.: P. Hartman and A. Wintner, On the local behavior of solutions of non-parabolic partial differential equations, ibid. (1953) pp. 449-476. MR 58082
41.: P. Hartman and A. Wintner, Umbilical points and W-surfaces, Amer. J. Math. vol. 76 (1954) pp. 502-508. MR 63082
42.: P. Hartman and A. Wintner , On the local behavior of solutions of non-parabolic partial differential equations, II; The uniqueness of the Green singularity, Amer. J. Math. vol. 76 (1954) pp. 351-361. MR 64271
43.: E. Heinz, Über die Eindeutigkeit beim Cauchyschen Anfangswertproblem einer elliptischen Differentialgleichung zweiter Ordnung, Nachrichten Goettingen, 1955, No. 1, pp. 1-12. MR 74666
44.: E. Hopf, Elementare Bemerkungen über Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus, Preuss. Akad. Wiss. Sitzungsber. vol. 19 (1927) pp. 147-152.
45.: F. John, The fundamental solution of linear elliptic differential equations with analytic coefficients, Comm. Pure Appl. Math. vol. 3 (1950) pp. 273-304. MR 42030
46.: S. Kakutani, On the family of pseudo-regular functions, Tôhoku Math. J. vol. 43 (1937) pp. 211-215.
47.: W. Kaplan, Topology of level curves of harmonic functions, Trans. Amer. Math. Soc. vol. 63 no. 3 (1948) pp. 514-522. MR 25159
48.: A. Kritszten, Hyperkomplexe und pseudo-analytische Funktionen, Comment. Math. Helv. vol. 26 (1952) pp. 6-35. MR 57348
49.: M. A. Lavrent'ev, A general problem of the theory of quasi-conformal representation of plane regions, Rec. Math. (Mat. Sbornik) N.S. vol. 21 (1947) pp. 285-320. MR 27342
50.: M. A. Lavrent'ev, A fundamental theorem of the theory of quasi-conformal mapping of plane regions, Izvestya Akademii Nauk SSSR. vol. 12 (1948) pp. 513-554. MR 34842
51.: C. Y. Lee, Similarity principle with boundary conditions for pseudo-analytic functions, Duke Math. J. vol. 23 (1956) pp. 157-163. MR 75314
52.: H. Lewy, On differential geometry in the large, I, Trans. Amer. Math. Soc. vol. 43 (1938) pp. 258-270. MR 1501942
53.: M. A. Lukomskaya, On one generalization of the class of analytic functions, C.R. (Doklady) Acad. Sci. URSS. vol. 73 (1950) pp. 885-888 (Russian). MR 39820
54.: M. A. Lukomskaya, On cycles of systems of linear homogeneous differential equations, Rec. Math. (Mat. Sbornik) N.S. vol. 29 (1951) pp. 551-558 (Russian). MR 52638
55.: M. A. Lukomskaya, Solution of some systems of partial differential equations by means of inclusion in a cycle, Akad. Nauk SSSR. Prikl. Mat. Meh. vol. 17 (1953) pp. 745-747 (Russian). MR 62913
56.: A. Miškis, Uniqueness of the solution of Cauchy's problem, Uspehi Matematičeskih Nauk vol. 3 (1948) pp. 3-46 (Russian).
57.: C. S. Morawetz, On the non-existence of continuous transonic flows past arbitrary profiles, I. Comm. Pure Appl. Math. vol. 9 (1956) pp. 45-68. MR 78130
58.: C. S. Morawetz, Uniqueness for the analogue of the Neumann problem for mixed equations, Michigan Math. J. (to appear). MR 85441
59.: C. B. Morrey, On the solutions of quasilinear elliptic partial differential equations, Trans. Amer. Math. Soc. vol. 43 (1938) pp. 126-166. MR 1501936
60.: M. Morse, Topological methods in the theory of functions of a complex variable, Annals of Mathematics Studies, no. 15, Princeton University Press, 1947. MR 21089
61.: M. Morse and M. Heins, Topological methods in the theory of functions of a complex variable, Ann. of Math. vol. 46 (1945) pp. 600-624, 625-666; vol. 47 (1946) pp. 233-274.
62.: M. Morse and M. Heins, Deformation classes of meromorphic functions and their extension to interior transformations, Acta. Math. vol. 78-79 (1947) pp. 51-103. MR 20128
63.: M. Morse, and J. A. Jenkins, Multiply-valued harmonic functions and their conjugates on arbitrary Riemann surfaces, Lectures on Functions of a Complex Variable, Michigan University Press, 1955, pp. 123-186.
64.: C. Müller, On the behavior of solutions of the differential equation Δ U = F(x, U) in the neighborhood of a point, Comm. Pure Appl. Math. vol. 7 (1954) pp. 505-515. MR 62920
65.: I. G. Petrovsky, On some problems in the theory of partial differential equations, Uspehi Matematičeskih Nauk vol. 1 (1946) pp. 44-70 (Russian). MR 27416
66.: A. Pfluger, Quasikonforme Abbildungen und logarithmische Kapazität, Annales de l'Institute Fourier, vol. 2 (1950) pp. 69-80. MR 44640
67.: E. Picard, Sur une système des équations aux dérivées partielles, C. R. Acad. Sci. Paris vol. 112 (1891) pp. 685-688.
68.: E. Picard, Sur une généralization des équations de la théorie des functions d'une variable complexe, ibid., pp. 1399-1403.
69.: G. N. Položii, On p-analytic functions of a complex variable, C. R. (Doklady) Acad. Sci. URSS. vol. 58 (1947) pp. 1275-1278 (Russian). MR 24523
70.: G. N. Položii, A generalization of Cauchy's integral formula, Math. Sbornik vol. 24 (1949) pp. 375-384 (Russian). MR 31571
71.: G. N. Položii, Singular points and residues of p-analytic functions of a complex variable, C. R. (Doklady) Acad. Sci. URSS. vol. 60 (1949) pp. 769-772 (Russian). MR 30007
72.: G. N. Položii, The theorem on preservation of domain for some elliptic systems of differential equations and its applications, Rec. Math. (Mat. Sbornik) N.S. vol. 32 (1953) pp. 485-492 (Russian). MR 58090
73.: M. H. Protter, Generalized spherical harmonics, Trans. Amer. Math. Soc. vol. 63 (1948) pp. 314-341. MR 24533
74.: M. H. Protter, The periodicity problem in the theory of pseudoanalytic functions, to appear in Ann. of Math.
75.: B. V. Šabat, Cauchy's theorem and formula for linear classes of quasi, C. R. (Doklady) Acad. Sci. URSS. vol. 69, (1949) pp. 305-308 (Russian). MR 36851
76.: Z. Schapiro, Sur l'existence des représentations quasiconformes, C. R. (Doklady) Acad. Sci. URSS. vol. 30 (1941) pp. 690-692. MR 4319
77.: L. Sobrero, Theorie der ebenen Elastizitaet unter Benutzung eines Systems hyperkomplexer Zahlen, Hamburger Mathematische Einzelschriften, Leipzig, 1934.
78.: S. Stoïlow, Leçons sur les principes topologiques de la théorie des fonctions analytiques, Paris, Gauthier-Villars, 1938.
79.: O. Teichmüller, Untersuchungen über konforme und quasikonforme Abbildungen, Deutsche Mathematik vol. 3 (1938) pp. 621-678.
80.: I. N. Vekua, New methods for solving elliptic equations, Moscow-Leningrad, 1948 (Russian). MR 34503
81.: I. N. Vekua, Systems of partial differential equations of first order of elliptic type and boundary value problems with applications to the theory of shells, Rec. Math. (Mat. Sbornik) N.S. vol. 31 (1952) pp. 217-314 (Russian). MR 57444
82.: I. N. Vekua, On a property of solutions of the system of generalized Cauchy-Riemann equations, Bull. Acad. Sci. Georgian SSR. vol. 14 (1953) pp. 449-453 (Russian). MR 72235
83.: I. N. Vekua, General representation of functions of two independent variables admitting derivatives in the sense of S. L. Sobolev, and the problem of primitives, C. R. (Doklady) Acad. Sci. URSS. vol. 89 (1953) pp. 773-775 (Russian). MR 57346
84.: I. N. Vekua, On some properties of solutions of systems of equations of elliptic type, C. R. (Doklady) Acad. Sci. URSS. vol. 98 (1954) pp. 181-184 (Russian). MR 70010
85.: A. Weinstein, Generalized axially symmetric potential theory, Bull. Amer. Math. Soc. vol. 59 (1953) pp. 20-38. MR 53289
86.: G. T. Whyburn, Introductory topological analsyis, Lectures on Functions of a Complex Variable, Michigan University Press, 1953, pp. 1-14. MR 70161
87.: Nachman Aronszajn, Sur l'unicité du prolongement des solutions des équations aux dérivées partielles elliptiques du second ordre, Comptes rendus vol. 242 (1956) pp. 723-725. MR 76155
88.: Lipman Bers, Formal powers and power series, Comm. Pure Appl. Math. vol. 9 (1956). MR 90739
89.: H. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math. vol. 88 (1952) pp. 85-139. MR 52553
90.: P. Hartman and A. Wintner, On the local behavior of solutions of non-parabolic partial differential equations. III: Approximations by spherical harmonics, Amer. J. Math. vol. 77 (1955) pp. 453-483. MR 76156
91.: E. M. Landis, On some properties of solutions of elliptic equations, Doklady Acad. Nauk SSSR. vol. 107 (1956) pp. 640-643 (Russian). MR 78557

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