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Faculty Member

John Wermer

Professor of Mathematics (Emeritis)


Office: 116 Kassar-Gould House
Phone: (401) 863-7059
Fax: (401) 863-9013
Email: wermer<at>

Mailing Address:

    Mathematics Department
    Box 1917
    Brown University
    Providence, RI 02912




Complex Analysis


Education: Ph.D., Harvard, 1951


Linking numbers and boundaries of varieties. Ann. of Math. (2) 151 (2000), no. 1, 125--150. w/Alexander, H.

Ando's theorem and sums of squares. Indiana Univ. Math. J. 48 (1999), no. 3, 767--791. w/Cole, Brian J.

Boundaries of interpolation bodies. Houston J. Math. 23 (1997), no. 3, 499--527. w/Cole, Brian J.

Several complex variables and Banach algebras. Third edition. Graduate Texts in Mathematics, 35. Springer-Verlag, New York, 1998. xii+253 pp. ISBN: 0-387-98253-1 w/Alexander, Herbert

Interpolation in the bidisk. J. Funct. Anal. 140 (1996), no. 1, 194--217. w/Cole, Brian J.

Isometries of certain operator algebras. Proc. Amer. Math. Soc. 124 (1996), no. 10, 3047--3053. w/Cole, Brian J.

Pick interpolation, von Neumann inequalities, and hyperconvex sets. Complex potential theory (Montreal, PQ, 1993), 89--129, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 439, Kluwer Acad. Publ., Dordrecht, 1994. w/Cole, Brian J.

Pick interpolation for a uniform algebra. Functional analysis and operator theory (Warsaw, 1992), 333--335, Banach Center Publ., 30, Polish Acad. Sci., Warsaw, 1994.

A characterization of Pick bodies. J. London Math. Soc. (2) 48 (1993), no. 2, 316--328. w/Cole, B.; Lewis, K.

Recollections of Arne Beurling. Math. Intelligencer 15 (1993), no. 3, 32--33.

Maximum modulus algebras. The Madison Symposium on Complex Analysis (Madison, WI, 1991), 469--478, Contemp. Math., 137, Amer. Math. Soc., Providence, RI, 1992.

Pick conditions on a uniform algebra and von Neumann inequalities. J. Funct. Anal. 107 (1992), no. 2, 235--254. w/Cole, Brian; Lewis, Keith

On the theorems of Pick and von Neumann. Function spaces (Edwardsville, IL, 1990), 273--280, Lecture Notes in Pure and Appl. Math., 136, Dekker, New York, 1992. w/Lewis, Keith

The collected works of Arne Beurling. Vol. 2. Harmonic analysis. Edited by L. Carleson, P. Malliavin, J. Neuberger and J. Wermer. Contemporary Mathematicians. Birkhäuser Boston, Inc., Boston, MA, 1989. xx+389 pp. ISBN: 0-8176-3416-9. Beurling, Arne

The collected works of Arne Beurling. Vol. 1. Complex analysis. Edited by L. Carleson, P. Malliavin, J. Neuberger and J. Wermer. Contemporary Mathematicians. Birkhäuser Boston, Inc., Boston, MA, 1989. xx+475 pp. ISBN: 0-8176-3415-0. Beurling, Arne

Function algebras in the fifties and sixties. A century of mathematics in America, Part III, 415--437, Hist. Math., 3, Amer. Math. Soc., Providence, RI, 1989.

Selected papers. With an introduction by John Wermer. World Scientific Publishing Co., Inc., Teaneck, NJ, 1986. xxvi+414 pp. ISBN: 9971-50-127-9. Bishop, Errett

Polynomial hulls of sets with intervals as fibers. Complex Variables Theory Appl. 11 (1989), no. 1, 11--19. w/Alexander, H.

Polynomial hulls and envelopes of holomorphy. Potential theory (Prague, 1987), 339--342, Plenum, New York, 1988.

Envelopes of holomorphy and polynomial hulls. Math. Ann. 281 (1988), no. 1, 13--22. w/Alexander, H.

Balayage and polynomial hulls. Complex analysis, II (College Park, Md., 1985--86), 303--312, Lecture Notes in Math., 1276, Springer, Berlin, 1987.

On the theorems of Hartogs and Bishop. Ann. Polon. Math. 46 (1985), 365--369.

On the approximation of singularity sets by analytic varieties. II. Michigan Math. J. 32 (1985), no. 2, 227--235. w/Alexander, H.

Polynomial hulls with convex fibers. Math. Ann. 271 (1985), no. 1, 99--109. w/Alexander, Herbert

Green's functions and polynomial hulls. Proceedings of the conference on Banach algebras and several complex variables (New Haven, Conn., 1983), 273--278, Contemp. Math., 32, Amer. Math. Soc., Providence, RI, 1984.

Linear algebra through geometry. Undergraduate Texts in Mathematics. Springer-Verlag, New York-Berlin, 1983. x+257 pp. ISBN: 0-387-90787-4 w/Banchoff, Thomas

On the approximation of singularity sets by analytic varieties. Pacific J. Math. 104 (1983), no. 2, 263--268. w/Alexander, Herbert

Polynomially convex hulls and analyticity. Ark. Mat. 20 (1982), no. 1, 129--135.

Potential theory and function algebras. Visiting scholars' lectures---1980 (Lubbock, Tex., 1980), pp. 113--125, Math. Ser., 14, Texas Tech Univ., Lubbock, Tex., 1981.

Orthogonal measures for subsets of the boundary of the ball in ${C}\sp{2}$. Recent developments in several complex variables (Proc. Conf., Princeton Univ., Princeton, N. J., 1979), pp. 277--289, Ann. of Math. Stud., 100, Princeton Univ. Press, Princeton, N.J., 1981. w/Lee, Hsuan Pei

Potential theory. Second edition. Lecture Notes in Mathematics, 408. Springer, Berlin, 1981. viii+166 pp. ISBN: 3-540-10276-0

Maximum modulus algebras and singularity sets. Proc. Roy. Soc. Edinburgh Sect. A 86 (1980), no. 3-4, 327--331.

On a domain equivalent to the bidisk. Math. Ann. 248 (1980), no. 3, 193--194.

Capacity and uniform algebras. Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978), Part 1, pp. 445--449, Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979.

{\cyr Teoriya potentsiala}. (Russian) [Potential theory] Translated from the English by V. V. Vavilov. ``Mir'', Moscow, 1980. 136 pp. 31-01 w/Uèrmer, D\v z.

Subalgebras of the disk algebra. Colloque d'Analyse Harmonique et Complexe, 7 pp. (not consecutively paged), Univ. Aix-Marseille I, Marseille, 1977.

Capacity and uniform algebras. J. Funct. Anal. 28 (1978), no. 3, 386--400. w/Aupetit, Bernard

Potential theory. Lecture Notes in Mathematics, Vol. 408. Springer-Verlag, Berlin-New York, 1974. viii+146 pp.

Fonctions sous-harmoniques et structure analytique du spectre des algèbres uniformes. (French) C. R. Acad. Sci. Paris Sér. A-B 284 (1977), no. 19, A1203--A1205. w/Aupetit, Bernard

Generators for $A(\Omega )$. Trans. Amer. Math. Soc. 194 (1974), 103--114. w/Sibony, N

Some rationally convex sets. Séminaire Goulaouic-Schwartz 1972--1973: Équations aux dérivées partielles et analyse fonctionnelle, Exp. No. 17, 5 pp. Centre de Math., École Polytech., Paris, 1973.

Banach algebras and several complex variables. Second edition. Graduate Texts in Mathematics, No. 35. Springer-Verlag, New York-Heidelberg, 1976. ix+161 pp.

Subharmonicity and hulls. Pacific J. Math. 58 (1975), no. 1, 283--290.

Approximation uniforme dans ${C}\sp{n}$. (French) Séminaire Pierre Lelong (Analyse) (année 1967--1968), pp. 165--166. Lecture Notes in Math., Vol. 71, Springer, Berlin, 1968.

Generators for the ball algebra. Seminar on Uniform Algebras (Univ. Aberdeen, Aberdeen, 1973), pp. 1--7. Dept. Math., Univ. Aberdeen, Aberdeen, 1973.

Banach algebras and several complex variables. Markham Publishing Co., Chicago, Ill., 1971. ix+129 pp. (loose errata).

On an example of Stolzenberg. Symposium on Several Complex Variables (Park City, Utah, 1970), pp. 79--84. Lecture Notes in Math., Vol. 184, Springer, Berlin, 1971.

Polynomial approximation. 1970 Proceedings of the Fifteenth Scandinavian Congress (Oslo, 1968), Lecture Notes in Mathematics, Vol. 118 pp. 133--162 Springer, Berlin

Uniform approximation on compact sets in $C\sp{n}$. Math. Scand. 23 1968 5--21 (1969). w/Hörmander, L

Banach algebras and uniform approximation. 1969 Lectures in Modern Analysis and Applications, I pp. 30--43 Springer, Berlin

Parts as finite-sheeted coverings of the disk. Amer. J. Math. 90 1968 98--107. w/O'Neill, B. V

Bounded point derivations on certain Banach algebras. J. Functional Analysis 1 1967 28--36.

Seminar über Funktionen-Algebren. (German) Winter-Semester 1963/64. Lecture Notes in Mathematics 1 Springer-Verlag, Berlin-Göttingen-Heidelberg 1964 iv+30 pp.

On two theorems of classical analysis. 1966 Function Algebras (Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965) pp. 84--87 Scott-Foresman, Chicago, Ill.

Dirichlet algebras. 1966 Contemporary Problems in Theory Anal. Functions (Internat. Conf., Erevan, 1965) (Russian) pp. 300--304 Izdat. "Nauka", Moscow

Maximal ideal spaces. 1963 Proc. Internat. Congr. Mathematicians (Stockholm, 1962) pp. 426--434 Inst. Mittag-Leffler, Djursholm

Polynomially convex disks. Math. Ann. 158 1965 6--10.

Errata: Remark on "Measures orthogonal to a Dirichlet algebra". Duke Math. J. 31 1964 717. w/Glicksberg, I.

Approximation on a disk. Math. Ann. 155 1964 331--333.

A method for constructing Dirichlet algebras. Proc. Amer. Math. Soc. 15 1964 546--552. w/Browder, A.

Analytic disks in maximal ideal spaces. Amer. J. Math. 86 1964 161--170.

The space of real parts of a function algebra. Pacific J. Math. 13 1963 1423--1426.

Measures orthogonal to a Dirichlet algebra. Duke Math. J. 30 1963 661--666. w/Glicksberg, I

A characterization of $C(X)$. Pacific J. Math. 12 1962 941--944. w/Hoffman, Kenneth

Some algebras of functions on an arc. J. Math. Mech. 12 1963 119--130. w/Browder, Andrew

Banach algebras and analytic functions. Advances in Math. 1 1961 fasc. 1, 51--102.

Subalgebras of $C(X)$. 1961 Proc. Internat. Sympos. Linear Spaces (Jerusalem, 1960) pp. 441--447 Jerusalem Academic Press, Jerusalem; Pergamon, Oxford

Dirichlet algebras. Duke Math. J. 27 1960 373--381.

The isometries of some function spaces. Proc. Amer. Math. Soc. 11 1960 694--698. w/de Leeuw, Karel; Rudin, Walter

Addendum to "An example concerning polynomial convexity". Math. Ann. 140 1960 322--323.

An example concerning polynomial convexity. Math. Ann. 139 1959 147--150 (1959).

On a subalgebra of $L(-\infty ,\,\infty )$. Amer. J. Math. 82 1960 103--105.

The maximum principle for bounded functions. Ann. of Math. (2) 69 1959 598--604.

The hull of a curve in $C\sp{n}$. Ann. of Math. (2) 68 1958 550--561.

Rings of analytic functions. Ann. of Math. (2) 67 1958 497--516.

Function rings and Riemann surfaces. Ann. of Math. (2) 67 1958 45--71.

Function rings on the circle. Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 173--175.

Subalgebras of the algebra of all complex-valued continuous functions on the circle. Amer. J. Math. 78 (1956), 225--242.

Report on subnormal operators. Report of an international conference on operator theory and group representations, Arden House, Harriman, N. Y., 1955, pp. 1--3. Publ. 387. National Academy of Sciences-National Research Council, Washingtion, D. C., 1955.

Maximal subalgebras of group-algebras. Proc. Amer. Math. Soc. 6 (1955), 692--694.

Polynomial approximation on an arc in $C\sp 3$. Ann of Math. (2) 62 (1955), 269--270.

Derivations on commutative normed algebras. Math. Ann. 129, (1955). 260--264. w/Singer, I. M

Invariant subspaces of bounded operators. Tolfte Skandinaviska Matematikerkongressen, Lund, 1953, pp. 314--316 Lunds Universitets Matematiska Institution, Lund, (1954).

Algebras with two generators. Amer. J. Math. 76, (1954). 853--859.

Commuting spectral measures on Hilbert space. Pacific J. Math. 4, (1954). 355--361.

On a class of normed rings. Ark. Mat. 2, (1954). 537--551.

On restrictions of operators. Proc. Amer. Math. Soc. 4, (1953). 860--865.

On algebras of continuous functions. Proc. Amer. Math. Soc. 4, (1953). 866--869.

Ideals in a class of commutative Banach algebras. Duke Math. J. 20, (1953). 273--278.

The existence of invariant subspaces. Duke Math. J. 19, (1952). 615--622.

On invariant subspaces of normal operators. Proc. Amer. Math. Soc. 3, (1952). 270--277.

Formulas and Theorems for the Special Functions of Mathematical Physics. Translated by John Wermer. Chelsea Publishing Company, New York, N.Y., 1949. viii+172 pp. Magnus, Wilhelm; Oberhettinger, Fritz

The work of Errett Bishop on several complex variables. Errett Bishop: reflections on him and his research (San Diego, Calif., 1983), 41--50, Contemp. Math., 39, Amer. Math. Soc., Providence, RI, 1985.