Analysis and topology : a volume dedicated to the memory of S. Stoilow

Cover......Page 1
S Title......Page 3
Analysis and Topology: A volume dedicated to the memory of S. Stoilow......Page 5
QA300A5492 1998 515--dc2l......Page 6
Simion Stoilow (1887„1961)......Page 7
FOREWORD......Page 8
CONTENTS......Page 10
BRIEF SUMMARY OF MY RESEARCH WORK*......Page 14
ON STOILOW'S WORK AND ITS INFLUENCE*......Page 22
1. General Topology......Page 27
2. Quasiregularity......Page 29
3. Riemann Surfaces......Page 30
4. Several Complex Variables......Page 32
A. REFERENCES ABOUT SIMION STOILOW LIST OF MATHEMATICAL PAPERS OF SIMION STOILOW......Page 33
MONOGRAPHS, TEXTBOOKS, COLLECTED WORKS......Page 37
SOME PAPERS ON SIMION STOILOW......Page 38
B. ADDITIONAL REFERENCES......Page 39
Introduction......Page 54
1. Preliminaries......Page 55
2. Characterization of the Hyperbolic Simply Connected Normally and E-quasinormally Coverings E = infininty and E = c1 delta......Page 57
3. Applications: Some Covering and Cluster Set Properties......Page 60
References......Page 62
1. Introduction......Page 66
2. Vectorial Approximation......Page 67
3. Vectorially Minimal Projections......Page 69
4. Some Special Cases......Page 71
5. Applications......Page 72
6. Feasibility and Convergence of the Algorithm......Page 73
References......Page 75
1. Introduction......Page 76
2. Schwarz Problem for Analytic Functions......Page 78
3. Inhomogeneous Cauchy-Riemann System......Page 82
4. Dirichiet Problem for Inhomogeneous Pluriharmonic System......Page 105
5. Riernann-Hjlbert Problem in the Unit Ball of C......Page 120
References......Page 126
1. Introduction......Page 128
2. Preliminaries......Page 130
3. Generalized Variational Inequalities......Page 133
4. Applications to Control Problems......Page 137
5.1. Quasi-variational inequalitites......Page 140
5.2. Complementarity problems......Page 146
5.3. Minimization and saddle points for non-smooth pseudoconvex functions......Page 148
References......Page 153
1. Introduction......Page 156
2. Further Study of the Zorn Spaces......Page 157
3. Connections with Classical Formulas......Page 159
References......Page 161
Goto 163 /FitH 555. Introduction......Page 164
1. Preliminaries......Page 166
2. Excessive Kernels......Page 168
3. Revuz Measures......Page 172
References......Page 175
1. Introduction......Page 178
2. Totally Increasing Functions on Ordered Sets......Page 180
3. Representable Totally Increasing Functions......Page 187
4. Totally Decreasing Functions on Ordered Sets......Page 193
5. Martin Boundary of an Ordered Set......Page 198
References......Page 202
Introduction......Page 204
References......Page 226
ABOUT CASES OF EQUALITY BETWEEN THE p-MODULE AND THE p-CAPACITY......Page 228
References......Page 252
Goto 253 /FitH 555. Introduction......Page 254
2. A Planar Dynamical System with a Trajectory of Infinite Lebesgue Measure......Page 255
3. A Non Arcwise Connected Limit Set......Page 256
4. A Planar (TR0)-System with Non-One-Point Limit Set Containing only Stationary Points......Page 258
5. A Stable but Non-orbitally Stable Singleton Set in a Semidynamical System......Page 260
6. Non-Removably Unstable Positively Invariant Sets......Page 262
References......Page 268
Goto 269 /FitH 555. Introduction......Page 270
1. Controlled Convergence, Control Functions......Page 271
2. Dirichiet Problem......Page 277
3. Lebesgue Derivation for Integrable Functions......Page 283
References......Page 288
A GENERALIZATION OF A THEOREM OF WEIERSTRASS......Page 290
References......Page 295
1. Introduction......Page 298
2. Préliminaires......Page 299
3. Demonstration du Théorème A......Page 301
Bibliographie......Page 303
Goto 305 /FitH 555. Introduction......Page 306
1. Mosaics......Page 307
2. Symbolic Dynamics......Page 318
References......Page 326
1. Introduction......Page 328
2. Harnack Functions......Page 330
3. Picard's Theorem......Page 335
References......Page 338
1. Introduction......Page 340
2. Estimate from above of the Rotation of a Welding Curve......Page 342
3. Proof of the Sufficiency in Theorem 1......Page 346
4. Proof of the Necessity in Theorem 1......Page 349
References......Page 351
1. Introduction......Page 352
2. Second Order Estimates......Page 357
3. Identities......Page 361
4. Second Order Equations......Page 365
5. Continuity of the Jacobian......Page 367
6. Computing the Jacobian......Page 369
7. Conclusion......Page 371
PSEUDOCONTINUOUS FUNCTIONS......Page 376
References......Page 373
LOCAL HARMONIC ANALYSIS FOR DOMAINS IN R^n OF FINITE MEASURE*......Page 390
1. Introduction......Page 391
2. Reproducing Kernels......Page 395
3. Hubert Space Frames......Page 398
5. Infinite Matrices Over the Set A......Page 405
6. Positive Definite Distributions......Page 407
7. The Ball in R^n......Page 409
8. The £2-Theory vs. the Continuous Case......Page 417
References......Page 420
SIMION STOILOW AND THE ROMANIAN MATHEMATICAL SCHOOL*......Page 424
References......Page 429
THE CONCEPT OF GLOBAL ANALYTIC FUNCTION AND RIEMANN SURFACE IN STOILOW'S WORK*......Page 430
1. Introduction......Page 438
2. Accidental Parabolic Transformations......Page 442
3. The Wrong Metric......Page 444
4. Simply Connected Invariant Open Sets......Page 447
5. Pinched Quasifuchsian Groups......Page 451
6. The Basic Trichotomy......Page 458
7. Degeneracy......Page 459
8. Deformation Spaces......Page 461
9. Existence of Degenerate Groups......Page 474
References......Page 476
1. Quasireflections......Page 480
2. Reflections over Holomorphic Curves......Page 482
3. Reflections over Analytic Arcs......Page 486
4. Pluricomplex Green Function and Holomorphic Extension......Page 487
6. Some Sufficient Conditions......Page 490
References......Page 492
DER KONFORME MODUL VON VIERECKEN......Page 496
Schriftt urn......Page 507
STOILOW'S WORK IN REAL ANALYSIS; ITS SIGNIFICANCE AND ITS IMPACT......Page 510
References......Page 516
THE ISOMORPHISM THEOREM OF KLEINIAN GROUPS......Page 520
References......Page 525
1. Introduction......Page 528
2. Classical Results......Page 529
3. Special Neighborhoods......Page 532
4. Embedded Morse Theory......Page 534
References......Page 535
1. Introduction......Page 538
2. Conditions for Starlikeness......Page 539
3. Conditions for Spiral-Likeness......Page 541
4. Conditions for Convexity and Alpha-Convexity......Page 543
5. Conditions for Close„to- Convexity......Page 545
References......Page 552
1. Introduction......Page 554
2. L-lengths......Page 556
3. Parametrizations of Teichmüller Spaces......Page 562
4. Parametrizations of Teichmüller Spaces T(g;mi,... ,m3) with s 1 by Geodesic Length Functions......Page 566
5. Teichmüller Space of Closed Surface of Genus 2......Page 570
References......Page 572
1. Introduction......Page 574
2. Norms and Laurent Expansion......Page 575
3. A Decomposition Theorem......Page 577
4. Construction of a Counterexample......Page 578
References......Page 579
1. Introduction......Page 582
2. Differentiability......Page 584
3. Generalized Bonvexity and Preliminaries......Page 586
4. Second Order Duality for (VP)......Page 588
References......Page 594
STABILITY AND SET-.VALUED FUNCTIONS......Page 598
1. Subquadratic and Quadratic Set-Valued Functions......Page 609
2. Comments......Page 623
Acknowledgments......Page 625
References......Page 626
1. The Modulus......Page 628
3. Steiner Symmetrization a la Pólya and Szegö......Page 630
4. Proof of the Theorem of Section 1......Page 631
References......Page 632
1. Introduction......Page 634
2. Quadratic Systems......Page 638
3. Cubic Systems......Page 651
4. Arbitrary Lage Polynomial Lage Systems......Page 652
References......Page 658
1. Introduction......Page 660
2. Quasimeromorphic Maps......Page 661
3. Möbius Groups......Page 662
References......Page 663
1. Introduction and Definitions......Page 666
2. Fractional Derivatives Associated with the Class $......Page 671
3. A Conjecture Involving the Class K......Page 675
4. Extensions Involving the Classes S*(a) and K(lpha)......Page 679
5. A New Class of Analytic Functions......Page 681
6. Further Extensions and Remarks......Page 683
References......Page 687
1. Introduction......Page 690
2. Examples......Page 694
3. Asymptotic Behaviour on Point Sequences......Page 695
4. Preservation of the Asymptotic Behaviour......Page 702
5. Existence of a Teichmüller Solution......Page 704
References......Page 708
2. Mapping Problems......Page 710
3. Spherical Rings......Page 717
4. Arc Distortion......Page 722
5. Characterizations of Free Quasiconformality......Page 726
References......Page 729
1. Introduction......Page 732
2. Proofs of Theorems 1 and 2......Page 734
3. A Necessary Condition for the General Problem......Page 735
References......Page 736
Back Cover......Page 737