VOLUME 325 NUMBER 2 JUNE 1991

WHOLE NUMBER 673

TransactionsJLoFTHE

AMERICAN MATHEMATICAL SOCIETY

EDITED BY

Avner D. Ash

James E. Baumgartner

James W. Cannon

Sun-Yung A. Chang

Ralph Cohen

Richard Durrett

David Jerison

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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1098 765432 1 96 95 94 93 92 91

INDEX TO VOLUME 325

May-June 1991

Akcoglu, M. A. and Bradley, R. E. Alternating sequences and induced operators, 765.

Alonso, Juan M. Quasi-projective and relative cohomological dimension of groups, 715.

Bardi, Martino and Soravia, Pierpaolo. Hamilton- Jacobi equations with singular boundary condi-

tions on a free boundary and applications to differential games, 205.

Bercovici, Hari, Foias, Ciprian and Tannenbaum, Allen. A spectral commutant lifting theorem,

741.

Borwein, J. M. and Lewis, A. S. On the convergence of moment problems, 249.

Bradley, R. E. See Akcoglu, M. A.

Bratteli, Ola and Robinson, Derek W. Second-order elliptic operators and heat kernels on Lie

groups, 683.Cox, J. T. and Griffin, Philip S. How porous is the graph of Brownian motion!, 119.

Dye, J., Khamsi, M. A. and Reich, S. Random products of contractions in Banach spaces, 87.

Evans, Steven N. and Perkins, Edwin. Absolute continuity results for superprocesses with some

applications, 661.Foias, Ciprian. See Bercovici, Hari

Froelich, John. Strictly cyclic operator algebras, 73.

Garofalo, Nicola and Segala, Fausto. New results on the Pompeiu problem, 273.

Grafakos, Loukas. Weak type estimates for a singular convolution operator on the Heisenberg group,435.

Griffin, Philip S. See Cox, J. T.Hall, Peter. A Picard theorem with an application to minimal surfaces. II, 895.

Hanlon, Phil. The generalized Dowling lattices, 1.

Ho, Lop-Hing. Subelliptic estimates for the d-Neumann problem for n - 1 forms, 111.

Hunt, Brian R. and Yorke, James A. Smooth dynamics on Weierstrass nowhere differentiable curves,

141.

Johannson, Klaus. On surfaces and Heegaard surfaces, 573.

Jungreis, Irwin. Some results on the Sarkovskii partial ordering of permutations, 319.

Khamsi, M. A. See Dye, J.

Kleene, S. C. Recursive functionals and quantifiers of finite types revisited, V, 593.

Landsberg, J. M. Minimal submanifolds o/E2"+1 arising from degenerate 50(3) orbits on the

Grassmannian, 101.

Lapidus, Michel L. Fractal drum, inverse spectral problems for elliptic operators and a partial res-

olution of the Weyl-Berry conjecture, 465.

Lau, Anthony To-Ming and Paterson, Alan L. T. Inner amenable locally compact groups, 155.

Lewis, A. S. See Borwein, J. M.

Lin, Huaxin. Support algebras ofa-unital C* -algebras and their quasi-multipliers, 829.

Loewen, Philip D. and Rockafellar, R. T. The adjoint arc in nonsmooth optimization, 39.

Monticino, Michael G. Utility functions which ensure the adequacy of stationary strategies, 187.

Morita, Takehiko. The symbolic representation of billiards without boundary condition, 819.

Nillsen, Rodney. Adapted sets of measures and invariant functionals on LP(G), 345.

Pate, Thomas H. Partitions, irreducible characters, and inequalities for generalized matrix func-tions, 875.

Paterson, Alan L. T. See Lau, Anthony To-Ming

Perkins, Edwin. See Evans, Steven N.

Phillips, N. Christopher. C°° loop algebras and noncommutative Bolt periodicity, 631.

Piergallini, R. Covering moves, 903.

Polterovich, L. V. The Maslov class of the Lagrange surfaces and Gromov's pseudo-holomorphiccurves, 241.

Rao, Ravi A. On completing unimodular polynomial vectors of length three, 231.

INDEX TO VOLUME 325

Reich, S. See Dye, J.Richter, Jürgen and Sturmfels, Bernd. On the topology and geometric construction of oriented ma-

troids and convex polytopes, 389.

Robinson, Derek W. See Bratteli, OlaRockafellar, R. T. See Loewen, Philip D.Scoppola, Carlo M. Groups of prime power order as Frobenius-Wielandt complements, 855.

Segala, Fausto. See Garofalo, Nicola

Shapiro, Victor L. Resonance and the second BVP, 363.

Sheingorn, Mark. Effective lower bounds for the norm of the Poincaré Q-operator, 453.

Snyder, David F. Partially acyclic manifold decompositions yielding generalized manifolds, 531.

Soravia, Pierpaolo. See Bardi, Martino

Sturmfels, Bernd. See Richter, Jürgen

Tannenbaum, Allen. See Bercovici, Hari

Wu, Ta-Sun. On the structure of certain locally compact topological groups, 413.

Yeh, R. Z. Hyperholomorphic functions and second order partial differential equations in R", 287.

Yorke, James A. See Hunt, Brian R.

Zhang, Shuang. Kygroups, quasidiagonality, and interpolation by multiplier projections, 793.

VOLUME 325 3 ífwf¡ ¡§ 1991

Transactions-A-OF THE

AMERICAN MATHEMATICAL SOCIETY

EDITED BY

Avner D. Ash

James E. Baumgartner

James W. Cannon

Sun-Yung A. Chang

Ralph Cohen

Richard Durrett

David Jerison

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 actingfor them, are permitted to make fair use of the material, such as to copy a chapter for use in teachingor research. Permission is granted to quote brief passages from this publication in reviews, providedthe customary acknowledgement of the source is given.

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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Contents

Vol. 325, No. 1 May 1991 Whole No. 672

The generalized Dowling lattices

By Phil Hanlon. 1

The adjoint arc in nonsmooth optimization

By Philip D. Loewen and R. T. Rockafellar. 39

Strictly cyclic operator algebras

By John Froelich. 73

Random products of contractions in Banach spaces

By J. Dye, M. A. Khamsi and S. Reich. 87

Minimal submanifolds of E2n+1 arising from degenerate S0(3) orbits on

the Grassmannian

By J. M. Landsberg . 101

How porous is the graph of Brownian motion?

By J. T. Cox and Philip S. Griffin . 119

Smooth dynamics on Weierstrass nowhere differentiable curves

By Brian R. Hunt and James A. Yorke. 141

Inner amenable locally compact groups

By Anthony To-Ming Lau and Alan L. T. Paterson. 155

Subelliptic estimates for the d -Neumann problem for n - 1 forms

By Lop-Hing Ho. 171

Utility functions which ensure the adequacy of stationary strategies

By Michael G. Monticino. 187

Hamilton-Jacobi equations with singular boundary conditions on a free

boundary and applications to differential games

By Martino Bardi and Pierpaolo Soravia. 205

On completing unimodular polynomial vectors of length three

By Ravi A. Rao. 231

The Maslov class of the Lagrange surfaces and Gromov's pseudo-holomorphic

curves

By L. V. Polterovich. 241

On the convergence of moment problems

By J. M. Borwein and A. S. Lewis . 249

New results on the Pompeiu problem

By Nicola Garofalo and Fausto Segala. 273

Hyperholomorphic functions and second order partial differential equa-

tions in R"

By R. Z. Yeh. 287

Some results on the Sarkovskii partial ordering of permutations

By Irwin Jungreis. 319

Adapted sets of measures and invariant functionals on LP(G)

By Rodney Nillsen . 345

Resonance and the second BVP

By Victor L. Shapiro. 363

On the topology and geometric construction of oriented matroids and con-

vex polytopes

By Jürgen Richter and Bernd Sturmfels . 389

On the structure of certain locally compact topological groups

By Ta-Sun Wu. 413

Weak type estimates for a singular convolution operator on the Heisenberg

group

By Loukas Grafakos. 435

Effective lower bounds for the norm of the Poincaré 8-operator

By Mark Sheingorn. 453

Vol. 325, No. 2 June 1991 Whole No. 673

Fractal drum, inverse spectral problems for elliptic operators and a partial

resolution of the Weyl-Berry conjecture

By Michel L. Lapidus . 465

Partially acyclic manifold decompositions yielding generalized manifolds

By David F. Snyder. 531

On surfaces and Heegaard surfaces

By Klaus Johannson. 573

Recursive functionals and quantifiers of finite types revisited, V

By S. C. Kleene. 593

C°° loop algebras and noncommutative Bott periodicity

By N. Christopher Phillips. 631

Absolute continuity results for superprocesses with some applications

By Steven N. Evans and Edwin Perkins. 661

Second-order elliptic operators and heat kernels on Lie groups

By Ola Bratteli and Derek W. Robinson. 683

Quasi-projective and relative cohomological dimension of groups

By Juan M. Alonso. 715

A spectral commutant lifting theorem

By Hari Bercovici, Ciprian Foias and Allen Tannenbaum. 741

Alternating sequences and induced operators

By M. A. Akcoglu and R. E. Bradley. 765

K\-groups, quasidiagonality, and interpolation by multiplier projections

By Shuang Zhang. 793

The symbolic representation of billiards without boundary condition

By Takehiko Morita. 819

Support algebras of rj-unital C* -algebras and their quasi-multipliers

By Huaxin Lin. 829

Groups of prime power order as Frobenius-Wielandt complements

By Carlo M. Scoppola. 855

Partitions, irreducible characters, and inequalities for generalized matrix

functions

By Thomas H. Pate. 875

A Picard theorem with an application to minimal surfaces. II

By Peter Hall. 895

Covering moves

By R. Piergallini. 903

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 sothat 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,

Department of Mathematics, The Ohio State University, 231 West 18th Avenue,

Columbus, OH 43210

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

Real and harmonic analysis to DAVID JERISON, Department of Mathematics,Room 2-180, Massachusetts Institute of Technology, Cambridge, MA 02139

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 ofMathematics, Brigham Young University, Provo, UT 84602

Algebraic topology and differential topology to RALPH COHEN, Department ofMathematics, 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 ofMathematics, University of Pennsylvania, El, Philadelphia, PA 19104-6395

Probability and statistics to RICHARD DURRETT, Department of Mathematics,Cornell University, Ithaca, NY 14853-7901

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, Hanover, NH

03755

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

Complex analysis and nonlinear partial differential equations to SUN-YUNG A.

CHANG, Department of Mathematics, University of California, Los Angeles, CA

90024

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

itor, DAVID J. SALTMAN, Department of Mathematics, University of Texas atAustin, Austin, TX 78713

COPYING AND REPRINTINGIndividual 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.

Requests for such permission should be addressed to the Manager of Editorial Services, 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.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Contents

Vol. 325, No. 2 June 1991 Whole No. 673

Fractal drum, inverse spectral problems for elliptic operators and a partial

resolution of the Weyl-Berry conjecture

By Michel L. Lapidus . 465

Partially acyclic manifold decompositions yielding generalized manifolds

By David F. Snyder . 531

On surfaces and Heegaard surfaces

By Klaus Johannson. 573

Recursive functionals and quantifiers of finite types revisited, V

By S. C. Kleene. 593

C°° loop algebras and noncommutative Bott periodicity

By N. Christopher Phillips. 631

Absolute continuity results for superprocesses with some applications

By Steven N. Evans and Edwin Perkins. 661

Second-order elliptic operators and heat kernels on Lie groups

By Ola Bratteli and Derek W. Robinson. 683

Quasi-projective and relative cohomological dimension of groups

By Juan M. Alonso. 715

A spectral commutant lifting theorem

By Hari Bercovici, Ciprian Foias and Allen Tannenbaum. 741

Alternating sequences and induced operators

By M. A. Akcoglu and R. E. Bradley. 765

Ä"]-groups, quasidiagonality, and interpolation by multiplier projections

By Shuang Zhang. 793

The symbolic representation of billiards without boundary condition

By Takehiko Morita. 819

Support algebras of er-unital C* -algebras and their quasi-multipliers

By Huaxin Lin. 829

Groups of prime power order as Frobenius-Wielandt complements

By Carlo M. Scoppola. 855

Partitions, irreducible characters, and inequalities for generalized matrix

functions

By Thomas H. Pate. 875

A Picard theorem with an application to minimal surfaces. II

By Peter Hall. 895

Covering moves

By R. Piergallini . 903