# Donald C Spencer's publications

The following is a fairly complete list of papers and books by

**Donald C Spencer**. We have omitted books which he edited.- D C Spencer, On a Hardy-Littlewood problem of diophantine approximation,
*Proc. Cambridge Philos. Soc.***35**(1939), 527-547.

- D C Spencer, On finitely mean valent functions. II,
*Trans. Amer. Math. Soc.***48**(1940), 418-435.

- D C Spencer, On an inequality of Grunsky,
*Proc. Nat. Acad. Sci. U.S.A.***26**(1940), 616-621.

- D C Spencer, Note on some function-theoretic identities,
*J. London Math. Soc.***15**(1940), 84-86.

- D C Spencer, On finitely mean valent functions,
*Proc. London Math. Soc. (2)***47**(1941), 201-211.

- D C Spencer, On a theorem of Rengels,
*J. Math. Phys., Massachusetts Inst.. Tech.***20**(1941), 118-123.

- D C Spencer, On distortion in analytic transformations,
*J. Math. Phys., Massachusetts Inst. Tech.***20**(1941), 124-126.

- D C Spencer, On mean one-valent functions,
*Ann. of Math.*(2)**42**(1941), 614-633.

- D C Spencer,
*Distortion in Conformal Mapping*(Brown University, 1941).

- D C Spencer, The lattice points of tetrahedra,
*J. Math, Phys., Massachusetts Inst. Tech.***21**(1942), 189-197.

- R Salem and D C Spencer, The influence of gaps on density of integers,
*Duke Math. J.***9**(1942), 855-872.

- R Salem and D C Spencer, On sets of integers which contain no three terms in arithmetical progression,
*Proc. Nat. Acad. Sci. U.S.A.***28**(1942), 561-563.

- D C Spencer, Note on mean one-valent functions,
*J. Math. Phys., Massachusetts Inst. Tech.***21**(1942), 178-188.

- D C Spencer, Some remarks concerning the coefficients of schlicht functions,
*J. Math. Phys., Massachusetts Inst. Tech.***21**(1942), 63-68.

- S Bergman and D C Spencer, On distortion in pseudo-conformal mapping,
*Trans. Amer. Math. Soc.***51**(1942), 133-163.

- S Bergman and D C Spencer, A property of pseudo-conformal transformations in the neighborhood of boundary points,
*Duke Math. J.***9**(1942), 757-762.

- D C Spencer, A function-theoretic identity,
*Amer. J. Math.***65**(1943), 147-160.

- A C Schaeffer and D C Spencer, The coefficients of schlicht functions,
*Duke Math. J.***10**(1943), 611-635.

- A C Schaeffer and D C Spencer, The coefficients of schlicht functions II,
*Duke Math. J.***12**(1945), 107-125.

- M Shiffman and D C Spencer,
*The Force of Impact on a Sphere Striking a Water Surface: Approximation by the Flow about a Lens,*Applied Math. Panel, National Defense Research Committee, Report No. 105 (Applied Mathematics Group, New York University, 1945).

- M Shiffman and D C Spencer,
*Second Approximation,*Applied Math. Panel, National Defense Research Committee, Report No. 133 (Applied Mathematics Group, New York University, 1945).

- A C Schaeffer and D C Spencer, The coefficients of schlicht functions III,
*Proc. Nat. Acad. Sci. U.S.A.***32**(1946), 111-115.

- A C Schaeffer and D C Spencer, A general class of problems in conformal mapping,
*Proc. Nat. Acad. Sci. U.S.A.***33**(1947), 185-189.

- D C Spencer, Some problems in conformal mapping,
*Bull. Amer. Math. Soc.***53**(1947), 417-439.

- A C Schaeffer and D C Spencer, A variational method in conformal mapping,
*Duke Math. J.***14**(1947), 949-966.

- M Shiffman and D C Spencer, The flow of an ideal incompressible fluid about a lens,
*Quart. Appl. Math.***5**(1947), 270-288.

- A C Schaeffer and D C Spencer, The coefficients of schlicht functions IV,
*Proc. Nat. Acad. Sci. U.S.A.***35**(1949), 143-150.

- A C Schaeffer, M Schiffer and D C Spencer, The coefficient regions of schlicht functions,
*Duke Math. J.***16**(1949), 493-527.

- R Salem and D C Spencer, On sets which do not contain a given number of terms in arithmetical progression,
*Nieuw Arch. Wiskunde*(2)**13**(1950), 133-143.

- M Schiffer and D C Spencer, The coefficient problem for multiply-connected domains,
*Ann. of Math.***52**(1950), 362-402.

- A C Schaeffer and D C Spencer, Models illustrating the third coefficient region for schlicht functions,
*Scripta Math.***16**(1950), 67-71.

- A C Schaeffer and D C Spencer,
*Coefficient Regions for Schlicht Functions,*Amer. Math. Soc. Colloq. Publ., Vol. 35 (New York, 1950).

- J A Jenkins and D C Spencer, Hyperelliptic trajectories,
*Ann. of Math.***53**(1951), 4-35.

- M Schiffer and D C Spencer, A variational calculus for Riemann surfaces,
*Ann. Acad. Sci. Fennicae. Ser. A I Math.-Phys.*(93) (1951).

- M Schiffer and D C Spencer, On the conformal mapping of one Riemann surface into another,
*Ann. Acad. Sci. Fennicae. Ser. A I Math.-Phys.*(94) (1951).

- G F D Duff and D C Spencer, Harmonic tensors on manifolds with boundary,
*Proc. Nat. Acad. Sci. U.S.A.***37**(1951), 614-619.

- M Shiffman and D C Spencer, The force of impact on a cone striking a water surface (vertical entry),
*Comm. Pure Appl. Math.***4**(1951), 379-417.

- A C Schaeffer and D C Spencer, Coefficient regions for schlicht functions,
*Proc. Internal. Congress Math.*(Cambridge, Mass., U.S.A., 1950), (Amer. Math. Soc., Vol. 2, 1952), 224-232.

- A C Schaeffer and D C Spencer, A variational method for simply-connected domains,
*Construction and applications of conformal maps,*Proc. Sympos., Nat. Bureau of Standards, (Applied Math. Ser. No. 18, 1952), 189-191.

- M Schiffer and D C Spencer, Some remarks on variational methods applicable to multiply-connected domains.
*Construction and applications of conformal maps,*Proc. Sympos., Nat. Bureau of Standards, (Applied Math. Ser. No. 18, 1952), 193-198.

- G F D Duff and D C Spencer, Harmonic tensors on Riemannian manifolds with boundary,
*Ann. of Math.***56**(1952), 128-156.

- P R Garabedian and D C Spencer, Complex boundary value problems,
*Trans. Amer. Math. Soc.***73**(1952), 223-242.

- D C Spencer, A generalization of a theorem of Hodge,
*Proc. Nat. Acad. Sci. U.S.A.***38**(1952), 533-534.

- D C Spencer,
*On Green's operators*(The Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park, Md., 1952).

- D C Spencer, Cauchy's formula on Kähler manifolds,
*Proc. Nat. Acad. Sci. U.S.A.***38**(1952), 76-80.

- P R Garabedian and D C Spencer, Extremal methods in cavitational flow,
*J. Rational Mech. Anal.***1**(1952), 359-409.

- P R Garabedian and D C Spencer, A complex tensor calculus for Kähler manifolds,
*Acta Math.***89**(1953), 279-331.

- D C Spencer, Heat conduction on arbitrary Riemannian manifolds,
*Proc. Nat. Acad. Sci U.S.A.***39**(1953), 327-330.

- D C Spencer, Real and complex operators on manifolds,
*Contributions to the theory of Riemann surfaces,*Annals of Math. Studies, No. 30 (Princeton University Press, 1953), 203-227.

- D C Spencer, Cohomology and the Riemann-Roch theorem,
*Proc. Nat. Acad. Sci. U.S.A.***39**(1953) 660-669.

- K Kodaira and D C Spencer, On arithmetic genera of algebraic varieties,
*Proc. Nat. Acad. Sci. U.S.A.***39**(1953), 641-649.

- K Kodaira and D C Spencer, Groups of complex line bundles over compact Kähler varieties,
*Proc. Nat. Acad. Sci. U.S.A.***39**(1953), 868-872.

- K Kodaira and D C Spencer, Divisor class groups on algebraic varieties,
*Proc. Nat. Acad. Sci. U.S.A.***39**(1953), 872-877.

- K Kodaira and D C Spencer, On a theorem of Lefschetz and the lemma of Enriques-Severi-Zariski,
*Proc. Nat. Acad. Sci. U.S.A.***39**(1953), 1273-1278.

- D C Spencer, Dirichlet's principle on manifolds,
*Studies in Math. and Mech. presented to Richard von Mises*(Academic Press, New York, 1954), 127-134.

- M Schiffer and D C Spencer,
*Functionals of finite Riemann surfaces*(Princeton University Press, 1954).

- D C Spencer, Potential theory and almost-complex manifolds,
*Lectures on functions of a complex variable*(University of Michigan Press, 1955), 15-43.

- V K A M Gugenheim and D C Spencer, Chain homotopy and the de Rham theory,
*Proc. Amer. Math. Soc.***7**(1956), 144-152.

- J J Kohn and D C Spencer,
*Complex Neumann problems on Kähler manifolds*(Princeton University, Princeton, N. J., 1956).

- J J Kohn and D C Spencer, Complex Neumann problems,
*Ann. of Math.***66**(1957), 89-140.

- K Kodaira and D C Spencer, On the variation of almost-complex structure,
*Algebraic Geometry and Topology*(Princeton University Press, 1957), 139-150.

- D C Spencer, A spectral resolution of complex structure,
*Sympos. Internac. Topologia Algebraica*(Mexico City, 1958), 68-76.

- K Kodaira and D C Spencer, On deformations of complex analytic structures I, II,
*Ann. of Math.***67**(1958), 328-466.

- K Kodaira, L Nirenberg and D C Spencer, On the existence of deformations of complex analytic structures,
*Ann. of Math.***68**(1958), 450-459.

- K Kodaira and D C Spencer, A theorem of completeness for complex analytic fibre spaces,
*Acta Math.***100**(1958), 281 -294.

- K Kodaira and D C Spencer, Existence of complex structure on a differentiable family of deformations of compact complex manifolds,
*Ann. of Math.***70**(1959), 145-166.

- K Kodaira and D C Spencer, A theorem of completeness of characteristic systems of complete continuous systems,
*Amer. J. Math.***81**(1959), 477-500.

- H K Nickerson, D C Spencer, and N E Steenrod,
*Advanced Calculus*(Van Nostrand, Princeton, New Jersey, 1959).

- D C Spencer, Some remarks on perturbation of structure,
*Analytic Functions*(Princeton University Press, 1960), 67-87.

- K Kodaira and D C Spencer, On deformations of complex analytic structures. III. Stability theorems for complex structures,
*Ann. of Math.***71**(1960), 43-76.

- L Nirenberg and D C Spencer, On rigidity of holomorphic imbeddings,
*Contributions to function theory*(Internal. Colloq. Function Theory) (Tata Institute, Bombay, 1960), 133-137.

- K Kodaira and D C Spencer, Multifoliate structures,
*Ann. of Math.***74**(1961), 52-100.

- D C Spencer, Some remarks on homological analysis and structures,
*Differential Geometry,*(Proc. Sympos. Pure Math. Vol. 3, Tucson, Arizona, 1960) (Amer. Math. Soc., 1961), 56-86.

- D C Spencer, Deformation of pseudogroup structures,
*Proc. Nat. Acad. Sci. U.S.A.***47**(1961), 1205-1208.

- D C Spencer, Complex analysis, article in the 1961 printing of the
*Encyclopaedia Britannica*(listed under Analysis, Complex).

- D C Spencer, A type of formal exterior differentiation associated with pseudogroups,
*Scripta Math.***26**(1961), 101-106.

- D C Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups I. Infinitesimal deformations of structure,
*Ann. of Math.***76**(1962), 306-398.

- D C Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups II. Deformations of structure,
*Ann. of Math.***76**(1962), 399-445.

- D C Spencer, Intrinsic formulation of the equation of structure of a transitive continuous pseudogroup,
*Studies in Math. Anal. and Related Topics*(Stanford University Press, Stanford Calif., 1962), 373-376.

- D C Spencer, Harmonic integrals and Neumann problems associated with linear partial differential equations.
*Outlines of the joint Soviet-American Sympos. on Partial Differential Equations,*August, 1963, Novosibirsk (Moscow, 1963), 253-260.

- D C Spencer, Correction to "Deformation of structures on manifolds defined by transitive, continuous pseudogroups. I. Infinitesimal deformations of structure".
*Ann. of Math.*(2)**78**(1963), 204.

- D C Spencer, De Rham theorems and Neumann decompositions associated with linear partial differential equations,
*Ann. Inst. Fourier (Grenoble)***14**(1964), 1-19.

- D C Spencer, Existence of local coordinates for structures defined by elliptic pseudo-groups,
*Differential Analysis*(Bombay Colloq. 1964), (Oxford University Press, 1964), 135-162.

- D C Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups, Part III: Structures defined by elliptic pseudogroups,
*Ann. of Math.***81**(1965), 389-450.

- D C Spencer, Remark on formal exterior differentiation,
*J. Analyse Math.***14**(1965), 433-442.

- D C Spencer, The theory of harmonic integrals,
*Some Recent Advances in the Basic Sciences,*Vol. 1, Annual Sci. Conf. Proc. Belfer Graduate School of Sci., (Yeshiva University, New York, 1966), 137-155.

- D C Spencer, Some remarks on overdetermined systems of linear partial differential equations,
*Proc. Katata Conf. on the theory of partial differential equations and on the theory of complex manifolds,*(Kyoto, 1966), 52-82.

- D C Spencer, Overdetermined systems of linear partial differential equations.
*Bull. Amer. Math. Soc.***75**(1969), 179-239.

- D C Spencer, On deformation of pseudogroup structures.
*Global Analysis*(Papers in honour of K Kodaira), (Princeton University Press, Princeton, N.J., 1969), 367-395.

- D C Spencer, Uncoupled overdetermined systems,
*Global Analysis,*Proc. Sympos. Pure Math. Vol. 16, Berkeley, California, 1968) (Amer. Math. Soc., Providence, R.I., 1970), 211-220.

- D C Spencer, Overdetermined operators: Some remarks on symbols,
*Proc. Internal. Congress Math.*Vol. 2, (Nice, France, 1970) (Gauthier-Villars, Paris, 1971), 251-256.

- D C Spencer, Flat differential operators, (Symposium on Several Complex Variables, Park City, Utah, 1970),
*Lecture Notes in Math.,*Vol. 184 (Springer Verlag, Berlin, 1971), 85-108.

- A Kumpera and D C Spencer,
*Lie Equations. Volume I: General Theory,*Annals of Math. Studies, No. 73 (Princeton University Press, 1972).

- A Kumpera and D C Spencer,
*Systems of Linear Partial Differential Equations and Deformation of Pseudogroup Structures,*Séminaire de Mathématiques Supérieure, 1969 (Presses de l'Université de Montréal, 1974)

- D C Spencer, Curvatures associated with differential operators, (Géométrie Différentielle, Colloq. Santiago de Compostella, Espagne, 1972), Lecture Notes in Math. Vol. 392, (Springer Verlag, Berlin, 1974), 64-75.

- D C Spencer, Construction of complexes for Lie equations,
*Manifolds-Tokyo*1973,*Proc. Internat. Conf. on Manifolds and Related Topics in Topology*(University of Tokyo Press, 1975), 303-311.

- H Goldschmidt and D C Spencer, On the non-linear cohomology of Lie equations. I,
*Acta Math.***136**(1976), 103-170.

- H Goldschmidt and D C Spencer, On the non-linear cohomology of Lie equations. II,
*Acta Math.***136**(1976) 171-239.

- H Goldschmidt and D C Spencer, Submanifolds and over-determined differential operators.
*Complex Analysis and Algebraic Geometry*(A collection of papers dedicated to K. Kodaira), (Iwanami Shoten Publishers and Cambridge University Press, 1977), 319-356.

- H Goldschmidt and D C Spencer, On the non-linear cohomology of Lie equations Ill,
*J. Differential Geometry***13**(1978) 409-453.

- H Goldschmidt and D C Spencer, On the non-linear cohomology of Lie equations IV,
*J. Differential Geometry***13**(1978), 455-526.

- D C Spencer, Kunihiko Kodaira (1915-1997),
*Notices Amer. Math. Soc.***45**(3) (1998), 388-389.

- D C Spencer,
*Selecta*Vol. 1 (World Scientific Publishing Co., Philadelphia, PA, 1985).

- D C Spencer,
*Selecta*Vol. 2 (World Scientific Publishing Co., Philadelphia, PA, 1985).

- D C Spencer,
*Selecta*Vol. 3 (World Scientific Publishing Co., Philadelphia, PA, 1985).

- D C Spencer, Old memories and an old problem,
*Prospects in mathematics (Princeton, NJ, 1996)*(Amer. Math. Soc., Providence, RI, 1999), 13-16.

Last Updated November 2006