VOLUME 320 NUMBER 2 AUGUST 1990

WHOLE NUMBER 663

TransactionsJLoFTHE

AMERICAN MATHEMATICAL SOCIETY

Avner D. Ash

James E. Baumgartner

James W. Cannon

Ralph Cohen

Burgess Davis

Eugene Fabes

Jerry L. Kazdan

Roger D. Nussbaum

Carl Pomerance

Judith D. Sally

David J. Saltman, Managing Editor

Masamichi Takesaki

Audrey Terras

PROVIDENCE, RHODE ISLAND USA

ISSN 0002-9947

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

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10 9 8 7 6 5 4 3 2 1 95 94 93 92 91 90

INDEX TO VOLUME 320

July-August 1990

Arino, Miguel A. and Muckenhoupt, Benjamin. Maximal functions on classical Lorentz spaces and

Hardy's inequality with weights for nonincreasing functions, 727.

Bass, Richard F. The Dirichlet problem for radially homogeneous elliptic operators, 593.

Benguria, Rafael D. and Yarur, Cecilia. Symmetry properties of the solutions to Thomas-Fermi-

Dirac-von Weizsacker type equations, 665.

Bergelson, Vitaly and Hindman, Neil. Nonmetrizable topological dynamics and Ramsey theory,

293.Bertsch, Michiel, Dal Passo, Roberta and Ughi, Maura. Discontinuous

"viscosity" solutions of a

degenerate parabolic equation, 119.

Bratteli, Ola, Kurose, Hideki and Robinson, Derek W. Comparison of commuting one-parameter

groups of isometries, 677.

Brown, Russell M. The initial-Neumann problem for the heat equation in Lipschitz cylinders, 1.

Clarke, F. H. and Vinter, R. B. A regularity theory for variational problems with higher order

derivatives, 227.

Connett, William C. and Schwartz, Alan L. Analysis of a class of probability preserving measure

algebras on compact intervals, 371.

Coomes, Brian A. Polynomial flows on C, 493.

Dal Passo, Roberta. See Bertsch, Michiel

Dillon, Meighan I. Weight strings in nonstandard representations of Kac-Moody algebras, 161.

Dugas, Manfred, Hill, Paul and Rangaswamy, K. M. Butler groups of infinite rank II, 643.

Faierman, M. Elliptic problems involving an indefinite weight, 253.

Gasharov, Vesselin N. and Peeva, Irena V. Boundedness versus periodicity over commutative local

rings, 569.Hill, Paul. See Dugas, Manfred

Hindman, Neil. See Bergelson, Vitaly

Iwase, Norio. A continuous localization and completion, 11.

Jackson, Steve. A new proof of the strong partition relation on wy, Til.

Konig, Hermann and Tomczak-Jaegermann, Nicole. Bounds for projection constants and 1 -summing

norms, 799.

Krantz, Steven G. On a theorem of Stein, 625.

Kurose, Hideki. See Bratteli, OlaLagarias, J. C. The nonlinear geometry of linear programming. III. Projective Legendre transform

coordinates and Hilbert geometry, 193.

Lewis, Jeff E. Layer potentials for elastostatics and hydrostatics in curvilinear polygonal domains,

53.Ma, Wenxin and Racine, Michel L. Minimal identities of symmetric matrices, 171.

Maitra, A., Purves, R. and Sudderth, W. Leavable gambling problems with unbounded utilities,

543.Marker, David. Semialgebraic expansions ofC, 581.

Mayer, John C. and Oversteegen, Lex G. A topological characterization ofR-trees, 395.Michalicek, Johannes and Wehrhahn, Rodolfo. Parametrization of domains in C: the logarithmic

domains, 765.

Muckenhoupt, Benjamin. See Arino, Miguel A.

Oversteegen, Lex G. See Mayer, John C.

Pang, Myung-Yull. The structure of Legendre foliations, 417.

Peeva, Irena V. See Gasharov, Vesselin N.

Profio, Joseph S. Using subnormality to show the simple connectivity at infinity of a finitely presented

group, 281.

Purisch, S. The orderability and closed images of scattered spaces, 713.

INDEX TO VOLUME 320

Purves, R. See Maitra, A.

Racine, Michel L. See Ma, Wenxin

Rahman, Qazi I. and Schmeisser, G. LP inequalities for entire functions of exponential type, 91.

Rangaswamy, K. M. See Dugas, Manfred

Robinson, Derek W. See Bratteli, Ola

Schmeisser, G. See Rahman, Qazi I.

Schroeder, V. and Ziller, W. Local rigidity of symmetric spaces, 145.

Schwartz, Alan L. See Connett, William C.

Sudderth, W. See Maitra, A.

Surace, Steve, Jr. The Schrodinger equation with a quasi-periodic potential, 321.

Tomczak-Jaegermann, Nicole. See Konig, Hermann

Ughi, Maura. See Bertsch, MichielVinter, R. B. See Clarke, F. H.Wehrhahn, Rodolfo. See Michalicek, JohannesYamagata, Shuji. Endomorphism rings of formal A$-modules, 615.

Yang, C. T. Smooth great circle fibrations and an application to the topological Blaschke conjecture,

507.Yarur, Cecilia. See Benguria, Rafael D.

Yin, Hong-Sheng. Classification of crossed-product C* -algebras associated with characters on free

groups, 105.

Yuen, David S. Second order theta functions and vector bundles over Jacobi varieties, 457.

Zalduendo, Ignacio. A canonical extension for analytic functions on Banach spaces, 747.

Ziegler, Gunter M. Matroid representations and free arrangements, 525.

Ziller, W. See Schroeder V.

Zimmermann-Huisgen, Birge and Zimmermann, Wolfgang. On the sparsity of representations of

rings of pure global dimension zero, 695.

Zimmermann, Wolfgang. See Zimmermann-Huisgen, Birge

0EM4JV

-(J/7i^^Zyk-VOLUME 320 tllflWl 199°

%5eo^

TransactionsJLofthe

american mathematical society

edited by

Avner D. Ash

James E. Baumgartner

James W. Cannon

Ralph Cohen

Burgess Davis

Eugene Fabes

Jerry L. Kazdan

Roger D. Nussbaum

Carl Pomerance

Judith D. Sally

David J. Saltman, Managing Editor

Masamichi Takesaki

Audrey Terras

PROVIDENCE, RHODE ISLAND USA_

ISSN 0002-9947

Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting

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The paper used in this book is acid-free and falls within the guidelinesestablished to ensure permanence and durability. @

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Contents

Vol. 320, No. 1 July 1990 Whole No. 662

The initial-Neumann problem for the heat equation in Lipschitz cylinders

By Russell M. Brown. 1

Layer potentials for elastostatics and hydrostatics in curvilinear polygonal

domains

By Jeff E. Lewis. 53

A continuous localization and completion

By Norio Iwase . 77

LP inequalities for entire functions of exponential type

By Qazi I. Rahman and G. Schmeisser. 91

Classification of crossed-product C* -algebras associated with characters on

free groups

By Hong-Sheng Yin. 105

Local rigidity of symmetric spaces

By V. Schroeder and W. Ziller. 145

Weight strings in nonstandard representations of Kac-Moody algebras

By Meighan I. Dillon. 161

Minimal identities of symmetric matrices

By Ma Wenxin and Michel L. Racine. 171

The nonlinear geometry of linear programming. III. Projective Legendre

transform coordinates and Hilbert geometry

By J. C. Lagarias. 193

A regularity theory for variational problems with higher order derivatives

By F. H. Clarke and R. B. Vinter. 227

Elliptic problems involving an indefinite weight

By M. Faierman. 253

Using subnormality to show the simple connectivity at infinity of a finitely

presented group

By Joseph S. Profio . 281

Nonmetrizable topological dynamics and Ramsey theory

By Vitaly Bergelson and Neil Hindman. 293

The Schrodinger equation with a quasi-periodic potential

By Steve Surace, Jr. 321

Analysis of a class of probability preserving measure algebras on compact

intervals

By William C. Connett and Alan L. Schwartz. 371

A topological characterization of R-trees

By John C. Mayer and Lex G. Oversteegen. 395

Vol. 320, No. 2 August 1990 Whole No. 663

The structure of Legendre foliations

By Myung-Yull Pang . 417

Second order theta functions and vector bundles over Jacobi varieties

By David S. Yuen. 457

Polynomial flows on C"

By Brian A. Coomes . 493

Smooth great circle fibrations and an application to the topological Blaschke

conjecture

By C. T. Yang. 507

Matroid representations and free arrangements

By Gunter M. Ziegler . 525

Leavable gambling problems with unbounded utilities

By A. Maitra, R. Purves and W. Sudderth. 543

Boundedness versus periodicity over commutative local rings

By Vesselin N. Gasharov and Irena V. Peeva. 569

Semialgebraic expansions of C

By David Marker. 581

The Dirichlet problem for radially homogeneous elliptic operators

By Richard F. Bass. 593

Endomorphism rings of formal ^-modules

By Shuji Yamagata. 615

On a theorem of Stein

By Steven G. Krantz . 625

Butler groups of infinite rank II

By Manfred Dugas, Paul Hill and K. M. Rangaswamy. 643

Symmetry properties of the solutions to Thomas-Fermi-Dirac-von Weiz-

sacker type equations

By Rafael D. Benguria and Cecilia Yarur. 665

Comparison of commuting one-parameter groups of isometries

By Ola Bratteli, Hideki Kurose and Derek W. Robinson. 677

On the sparsity of representations of rings of pure global dimension zero

By Birge Zimmermann-Huisgen and Wolfgang Zimmermann .. 695

The orderability and closed images of scattered spaces

By S. Purisch . 713

Maximal functions on classical Lorentz spaces and Hardy's inequality with

weights for nonincreasing functions

By Miguel A. Arino and Benjamin Muckenhoupt. 727

A new proof of the strong partition relation on a>i

By Steve Jackson. 737

A canonical extension for analytic functions on Banach spaces

By Ignacio Zalduendo. 747

Parametrization of domains in C: the logarithmic domains

By Johannes MichaliCek and Rodolfo Wehrhahn. 765

Discontinuous "viscosity"

solutions of a degenerate parabolic equation

By Michiel Bertsch, Roberta Dal Passo and Maura Ughi_ 779

Bounds for projection constants and 1-summing norms

By Hermann Konig and Nicole Tomczak-Jaegermann. 799

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETYThis bimonthly journal is devoted to research in pure and applied mathematics of much the same

nature as appears in TRANSACTIONS. An issue consists of one or more separately bound research

tracts for which the author(s) has provided reproduction copy. Prior to 1975 this was publishedas a monograph series. The editorial committee is identical with that for the TRANSACTIONS so

that papers intended for publication in this series should be addressed to one of the editors.

SUBMISSION OF MANUSCRIPTTwo copies of mathematical papers intended for publication in the TRANSACTIONS or theMEMOIRS should be addressed to one of the editors. Subjects, and the editors associated with

them, follow.

Harmonic analysis, representation theory, and Lie theory to AVNER D. ASH, De-

partment of Pure Mathematics and Mathematical Statistics, University of Cam-

bridge, 16 Mill Lane, Cambridge, CB2 1SB, England

Abstract analysis to MASAMICHI TAKESAKI, Department of Mathematics, Uni-versity of California, Los Angeles, CA 90024

Classical analysis (including complex, real, and harmonic) to EUGENE FABES,

Department of Mathematics, University of Minnesota, Minneapolis, MN 55455

Algebra and algebraic geometry to JUDITH D. SALLY, Department of Mathemat-ics, Northwestern University, Evanston, IL 60208

Geometric topology and general topology to JAMES W. CANNON, Department of

Mathematics, Brigham Young University, Provo, UT 84602

Algebraic topology and differential topology to RALPH COHEN, Department of

Mathematics, Stanford University, Stanford, CA 94305

Ordinary differential equations, partial differential equations, and applied mathe-

matics to ROGER D. NUSSBAUM, Department of Mathematics, Rutgers Univer-

sity, New Brunswick, NJ 08903

Global analysis and differential geometry to JERRY L. KAZDAN, Department of

Mathematics, University of Pennsylvania, El, Philadelphia, PA 19104-6395

Probability and statistics to BURGESS DAVIS, Departments of Mathematics and

Statistics, Purdue University, West Lafayette, IN 47907

Combinatorics and number theory to CARL POMERANCE, Department of Math-

ematics, University of Georgia, Athens, GA 30602

Logic, set theory, general topology, and universal algebra to JAMES E. BAUM-

GARTNER, Department of Mathematics, Dartmouth College, Hannover, NH

37550

Algebraic number theory, analytic number theory, and modular forms to AUDREY

TERRAS, Department of Mathematics, University of California at San Diego, La

Jolla, CA 92093

All other communications to the editors should be addressed to the Managing Ed-

itor, DAVID J. SALTMAN, Department of Mathematics, University of Texas at

Austin, Austin, TX 78713

COPYING AND REPRINTING

Individual readers of this publication, and nonprofit libraries acting for them, are permitted to

make fair use of the material, such as to copy an article for use in teaching or research. Permis-

sion is granted to quote brief passages from this publication in reviews, provided the customary

acknowledgment of the source is given.Republication, systematic copying, or multiple reproduction of any material in this publication

(including abstracts) is permitted only under license from the American Mathematical Society. Re-

quests for such permission should be addressed to the Executive Director, American Mathematical

Society, P.O. Box 6248, Providence, Rhode Island 02940-6248.The appearance of the code on the first page of an article in this journal indicates the copyright

owner's consent for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright

Law, provided that the fee of $1.00 plus $.25 per page for each copy be paid directly to the Copy-

right Clearance Center, Inc., 27 Congress Street, Salem, Massachusetts 01970. This consent does

not extend to other kinds of copying, such as copying for general distribution, for advertising or

promotional purposes, for creating new collective works, or for resale.

(Continued from back cover)

Maximal functions on classical Lorentz spaces and Hardy's inequality with

weights for nonincreasing functions

By Miguel A. Arino and Benjamin Muckenhoupt. 727

A new proof of the strong partition relation on co\

By Steve Jackson. 737

A canonical extension for analytic functions on Banach spaces

By Ignacio Zalduendo. 747

Parametrization of domains in C: the logarithmic domains

By Johannes MichaliCek and Rodolfo Wehrhahn. 765

Discontinuous "viscosity" solutions of a degenerate parabolic equation

By Michiel Bertsch, Roberta Dal Passo and Maura Ughi_ 779

Bounds for projection constants and 1-summing norms

By Hermann Konig and Nicole Tomczak-Jaegermann. 799

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Contents

Vol. 320, No. 2 August 1990 Whole No. 663

The structure of Legendre foliations

By Myung-Yull Pang . 417

Second order theta functions and vector bundles over Jacobi varieties

By David S. Yuen. 457

Polynomial flows on C"

By Brian A. Coomes . 493

Smooth great circle fibrations and an application to the topological Blaschke

conjecture

By C. T. Yang. 507

Matroid representations and free arrangements

By Gunter M. Ziegler . 525

Leavable gambling problems with unbounded utilities

By A. Maitra, R. Purves and W. Sudderth. 543

Boundedness versus periodicity over commutative local rings

By Vesselin N. Gasharov and Irena V. Peeva. 569

Semialgebraic expansions of C

By David Marker. 581

The Dirichlet problem for radially homogeneous elliptic operators

By Richard F. Bass. 593

Endomorphism rings of formal ,4n-modules

By Shuji Yamagata. 615

On a theorem of Stein

By Steven G. Krantz . 625

Butler groups of infinite rank II

By Manfred Dugas, Paul Hill and K. M. Rangaswamy. 643

Symmetry properties of the solutions to Thomas-Fermi-Dirac-von Weiz-

sacker type equations

By Rafael D. Benguria and Cecilia Yarur. 665

Comparison of commuting one-parameter groups of isometries

By Ola Bratteli, Hideki Kurose and Derek W. Robinson. 677

On the sparsity of representations of rings of pure global dimension zero

By Birge Zimmermann-Huisgen and Wolfgang Zimmermann .. 695

The orderability and closed images of scattered spaces

By S. Purisch . 713

(Continued on inside back cover)