Ergebnisse der Mathematik und ihrer Grenzgebiete

Os Ergebnisse der Mathematik und ihrer Grenzgebiete (tradução literal do alemão: "Resultadoss im matemática e suas áreas relacionadas") são uma série de monografias matemáticas da Springer Verlag. Começou em 1932 com o volume Knotentheorie de Kurt Reidemeister. A segunda série (com no total 101 volumes) começou em 1955 com o volume Transfinite Zahlen de Heinz Bachmann e a terceira série em 1983. A série recebeu mais tarde o complemento em inglês A series of modern surveys in mathematics.

Parte principal, história

Foi fundada em 1932 pelos editores do Zentralblatt MATH, dentre os quais Pavel Alexandrov, Wilhelm Blaschke, Richard Courant, Godfrey Harold Hardy, Gaston Julia, Tullio Levi-Civita, Rolf Nevanlinna e Bartel Leendert van der Waerden. Inicialmente com cinco contribuições por volume, que correspondiam a uma publicação semelhante a um periódico com artigos de ampla revisão com um máximo de 100 a 150 páginas.^[1] Na época do nazismo os volumes começaram a ser publicados irregularmente a partir de 1936. A primeira série terminou em 1942 (com o último número do quinto volume).

Após a Segunda Guerra Mundial foi decidido publicar livros individuais (cadernos). Como editores no primeiro volume da segunda série (publicado em 1955) foram declarados: Lars Valerian Ahlfors (responsável por análise complexa), Reinhold Baer (teoria de grupos), Richard Courant, Joseph Leo Doob (probabilidade e estatística), Samuel Eilenberg (topologia), Hans Rademacher, Friedrich Karl Schmidt, Beniamino Segre (geometria algébrica) e Emanuel Sperner. Responsável por análise foi Paul Halmos. Cada um dos editores podia propor projetos de livros em sua área. Até 1961 foram publicados 30 volumes. A partir de 1961 Peter Hilton foi editor e os livros individuais apresentados então como volumes ao invés de cadernos. Em 1968 os editores eram Paul Halmos, Reinhold Remmert, Peter Hilton e Béla Szőkefalvi-Nagy^[2] (com a colaboração de Courant, Ahlfors, Baer, Doob, Eilenberg, Rademacher, Sperner, B. Segre, Albrecht Dold, Martin Kneser, Mikhail Postnikov, Friedrich Ludwig Bauer e Gert Heinz Müller). O último volume da segunda série (No. 101) apareceu em 1988. Mais tarde foram publicadas reimpressões.

A terceira série foi iniciada na década de 1970, com Reinhold Remmert como editor principal, que fundou antes com sucesso o periódico Inventiones Mathematicae e de lá introduzia a terceira série (como Jacques Tits, Jean-Pierre Serre, Nicolaas Kuiper e Enrico Bombieri). O primeiro volume foi publicado em 1983. Até 2017 foram publicados 67 volumes na terceira série. Não existe um editor principal.

Volumes reconhecidos foram por exemplo Fastperiodische Funktionen por Harald Bohr (1932), Algebren por Max Deuring (1935), Algebraic Surfaces por Oscar Zariski (1935), Theorie der Funktionen mehrerer komplexer Veränderlichen por Heinrich Behnke e Peter Thullen (1934), Grundbegriffe der Wahrscheinlichkeitsrechnung por Andrei Kolmogorov (1933), On the problem of Plateau por Tibor Radó (1933), Idealtheorie por Wolfgang Krull (1935), Ergodentheorie por Eberhard Hopf (1937), Diophantische Approximationen por Jurjen Ferdinand Koksma (1936), Neue topologische Methoden in der algebraischen Geometrie por Friedrich Hirzebruch (1956), Generators and relations for discrete groups por Harold Scott MacDonald Coxeter e William Oscar Jules Moser (1957), Inequalities por Edwin Ford Beckenbach e Richard Bellman, Geometric Invariant Theory (1965) por David Mumford, Finite Geometries (1968) por Peter Dembowski e Coding Theorems of Information Theory por Jacob Wolfowitz (1961).

O ISSN da terceira série é 0071-1136.

Volumes da primeira série

Novas edições dos volumes por Krull, Deuring, Zariski e Behnke/Thullen foram lançados na segunda série

1,1 Kurt Reidemeister: Knotentheorie 1932
1,2 Karl Federhofer: Graphische Kinematik und Kinetostatik, 1932
1,3 Max Strutt: Lamésche-, Mathieusche- und verwandte Funktionen in Physik und Technik, 1932
1,4 Kurt Hohenemser: Die Methoden zur angenäherten Lösung von Eigenwertproblemen in der Elastokinetik, 1932
1,5 Harald Bohr: Fastperiodische Funktionen, 1932
2,1 Oswald Veblen: Projektive Relativitätstheorie, 1933
2,2 Tibor Radó: On the problem of Plateau, 1933
2,3 Andrei Kolmogorov: Grundbegriffe der Wahrscheinlichkeitstheorie, 1933
2,4 Aleksandr Khinchin: Asymptotische Gesetze der Wahrscheinlichkeitsrechnung, 1933
2,5 Cyrus Colton MacDuffee: The theory of matrices, 1933
3,1 Tommy Bonnesen: Theorie der konvexen Körper, 1934
3,2 Dirk Jan Struik: Theory of linear connections, 1934
3,3 Heinrich Behnke, Peter Thullen: Theorie der Funktionen mehrerer komplexer Veränderlichen, 1934
3,4 Arend Heyting: Mathematische Grundlagenforschung, Intuitionismus, Beweistheorie, 1934
3,5 Oscar Zariski: Algebraic Surfaces, 1935
4,1 Max Deuring: Algebren 1935
4,2 Bartel Leendert van der Waerden: Gruppen von linearen Transformationen, 1935
4,3 Wolfgang Krull: Idealtheorie, 1935
4,4 Jurjen Ferdinand Koksma: Diophantische Approximationen, 1936
4,5 Constantin Carathéodory: Geometrische Optik, 1937
5,1 Tibor Radó; Subharmonic Functions, 1937
5,2 Eberhard Hopf: Ergodentheorie, 1937
5,3 Hans Ertel: Methoden und Probleme der dynamischen Meteorologie 1938
5,4 Thoralf Skolem: Diophantische Gleichungen, 1938
5,5 Béla Szőkefalvi-Nagy: Spektraldarstellung linearer Transformationen des Hilbertschen Raumes, 1942

Volumes da segunda série

1 Heinz Bachmann: Transfinite Zahlen 1955
2 Carlo Miranda: Equazioni alle derivate parziali di tipo ellittico, 1955, 2. Auflage 1970: Partial differential equations of elliptic type
3 Ludwig Bieberbach: Analytische Fortsetzung, 1955
4 Pierre Samuel: Méthodes d'Algèbre Abstraite en Géométrie Algébrique, 1955, 2. Auflage 1967
5 Jean Dieudonné: La géométrie des groupes classiques, 1955, 2. Auflage 1963
6 Leonard Roth: Algebraic threefolds : with special regard to problems of rationality, 1955
7 Hans-Heinrich Ostmann: Additive Zahlentheorie, Band 1, 1956, 2. Auflage 1968
8 Hans Wittich: Neuere Untersuchungen über eindeutige analytische Funktionen, 1956, 2. Auflage 1968
9 Friedrich Hirzebruch: Neue topologische Methoden in der algebraischen Geometrie, 1956, 2. Auflage 1962
10 Michio Suzuki: Structure of a group and the structure of its lattice of subgroups, 1956
11 Hans-Heinrich Ostmann: Additive Zahlentheorie, Band 2, 1956
12 Mario Baldassarri: Algebraic Varieties, 1956
13 Beniamino Segre: Some properties of differentiable varieties and transformations : with special reference to the analytic and algebraic cases, 1957
14 H. S. M. Coxeter, W. O. J. Moser: Generators and relations for discrete groups, 1957, 4. Auflage 1980
15 Karl Longin Zeller: Theorie der Limitierungsverfahren, 1958, 2. Auflage 1970
16 Lamberto Cesari: Asymptotic behavior and stability problems in ordinary differential equations, 1959, 2. Auflage 1963
17 Francesco Severi: Il teorema di Riemann-Roch per curve, superficie e varietà : questioni collegate, 1958
18 James A. Jenkins: Univalent functions and conformal mapping, 1958, 2. Auflage 1965
19 Ralph Boas, Robert Creighton Buck: Polynomial expansions of analytic functions, 1958, 2. Auflage 1964
20 Richard Bruck: Survey of binary systems, 1958, 3. Auflage 1971
21 Mahlon M. Day: Normed linear spaces, 1958, 2. Auflage 1962
22 Wolfgang Hahn: Theorie und Anwendung der direkten Methode von Ljapunow, 1959
23 Stefan Bergman: Integral operators in the theory of linear partial differential equations, 1961, 2. Auflage 1969
24 Demetrios Kappos: Strukturtheorie der Wahrscheinlichkeitsfelder und -räume, 1960
25 Roman Sikorski: Boolean Algebras, 1960, 2. Auflage 1964
26 Hans Künzi: Quasikonforme Abbildungen, 1960
27 Robert Schatten: Norm ideals of completely continuous operators, 1960
28 Kiyoshi Noshiro: Cluster Sets, 1960
29 Konrad Jacobs: Neuere Methoden und Ergebnisse der Ergodentheorie 1960
30 Edwin Beckenbach, Richard Bellman: Inequalities, 1961, 2. Auflage 1965
31 Jacob Wolfowitz: Coding theorems of information theory, 1961, 3. Auflage 1978
32 Corneliu Constantinescu: Ideale Ränder Riemannscher Flächen, 1963
33 Pierre Conner, Edwin Floyd: Differentiable periodic maps, 1964
34 David Mumford: Geometric Invariant Theory, 1965, 2. Auflage 1982, 3. Auflage 1994
35 Peter Gabriel: Calculus of fractions and homtopy theory, 1967
36 Calvin Richard Putnam: Commutation properties of Hilbert space operators and related topics, 1967
37 Hanna Neumann: Varieties of Groups, 1967
38 Ralph Boas: Integrability theorems for trigonometric transforms, 1967
39 Béla Szőkefalvi-Nagy: Spektraldarstellung linearer Transformationen des Hilbertschen Raumes, 1967
40 George Seligman: Modular Lie Algebras, 1967
41 Max Deuring: Algebren, 2. Auflage 1967
42 Kurt Schütte: Vollständige Systeme modaler und intuitionistischer Logik, 1968
43 Raymond Smullyan: First order logic, 1968 (Nachdruck Dover 1995)
44 Peter Dembowski: Finite Geometries, 1968
45 Juri Linnik: Ergodic properties of algebraic fields, 1968
46 Wolfgang Krull: Idealtheorie, 2. Auflage 1968
47 Leopoldo Nachbin: Topology on spaces of holomorphic mappings, 1969
48 A. Ionescu Tulcea, Cassius Ionescu Tulcea: Topics in the theory of lifting 1969
49 Charles A. Hayes, Christian Y. Pauc: Derivation and Martingales, 1970
50 Jean-Pierre Kahane: Séries de Fourier absolument convergentes, 1970
51 Heinrich Behnke, Peter Thullen: Theorie der Funktionen mehrerer komplexer Veränderlichen, 2. Auflage, Hrsg. Reinhold Remmert
52 Herbert Wilf: Finite sections of some classical inequalities, 1970
53 Jean-Pierre Ramis: Sous-ensembles analytiques d'une variété banachique complexe, 1970
54 Herbert Busemann: Recent synthetic differential geometry, 1970
55 Wolfgang Walter: Differential and integral inequalities, 1970
56 Antonie Frans Monna: Analyse non-archimédienne, 1970
57 Erik Alfsen: Compact convex sets and boundary integrals, 1971
58 Silvio Greco, Paolo Salmon: Topics in m-adic topologies, 1971
59 Santiago López de Medrano: Involutions on manifolds, 1971
60 Shōichirō Sakai: C*-algebras and W*-algebras, 1971
61 Oscar Zariski: Algebraic Surfaces, 2. Auflage 1971, mit Appendices von S. S. Abhyankar, Joseph Lipman und David Mumford
62, 63 Derek J. S. Robinson: Finiteness conditions and generalized soluble groups, Teil 1, 2, 1972
64 Monique Hakim: Topos annelés et schémas relatifs, 1972
65 William Browder: Surgery on simply-connected manifolds, 1972
66 Albrecht Pietsch: Nuclear locally convex spaces, 1972
67 Claude Dellacherie: Capacités et processus stochastiques, 1972
68 M. S. Raghunathan: Discrete subgroups of Lie groups, 1972
69 Colin Rourke, Brian J. Sanderson: Introduction to piecewise-linear topology, 1972
70 Shoshichi Kobayashi: Transformation groups in differential geometry, 1972
71 Jean Claude Tougeron: Idéaux de fonctions différentiables, 1972
72 Iossif Iljitsch Gichman, Anatoli Skorochod: Stochastic differential equations, 1972
73 John Milnor: Symmetric bilinear forms, 1973
74 Robert Fossum: The divisor class group of a Krull domain, 1973
75 Tonny Springer: Jordan algebras and algebraic groups, 1973
76 Bertram Wehrfritz: Infinite linear groups : an account of the group-theoretic properties of infinite groups of matrices, 1973
77 Heydar Radjavi, Peter Rosenthal: Invariant Subspaces, 1973
78 János Bognár: Indefinite inner product spaces, 1974
79 Anatoli Skorochod: Integration in Hilbert Space, 1974
80 Frank Featherstone Bonsall, John Duncan: Complete normed algebras, 1973
81 John Crossley, Anil Nerode: Combinatorial functors, 1974
82 Walentin Wladimirowitsch Petrow (Valentin V. Petrov): Sums of independent random variables, 1975
83 Russell C. Walker: The Stone-Čech compactification, 1974
84 James Howard Wells, Lynn R. Williams: Embeddings and extensions in analysis, 1975
85 Wu Yi Hsiang: Cohomology theory of topological transformation groups, 1975
86 Alexander Olewski: Fourier series with respect to general orthogonal systems, 1975
87 Christian Berg, Gunnar Forst: Potential theory on locally compact Abelian groups, 1975
88 André Weil: Elliptic functions according to Kronecker and Eisenstein, 1976
89 Roger Lyndon, Paul E. Schupp: Combinatorial group theory, 1977
90 Robert E. Edwards, Garth Gaudry: Littlewood-Paley and multiplier theory, 1977
91 Robert Gunning: Riemann surfaces and generalized theta functions, 1976
92 Joram Lindenstrauss, Lior Tzafriri: Classical Banach spaces 1: Sequence spaces, 1977
93 Arthur Besse: Manifolds all of whose geodesics are closed, 1978
94 Herbert Heyer: Probability measures on locally compact groups 1977
95 Sergei Adian: The Burnside problem and identities in groups, 1979
96 Paul Halmos, V. S. Sunder: Bounded integral operators on L2 spaces, 1978
97 Joram Lindenstrauss, Lior Tzafriri: Classical Banach spaces 2: Function spaces, 1979
98 Sibylla Prieß-Crampe: Angeordnete Strukturen : Gruppen, Körper, projektive Ebenen, 1983
99 Bruce L. Reinhart: Differential geometry of foliations : the fundamental integrability problem, 1983
100 Hans Petersson: Modulfunktionen und quadratische Formen, 1982
101 Ramesh Gangolli, V. S. Varadarajan: Harmonic analysis of spherical functions on real reductive groups, 1988

Volumes da terceira série

1 Albrecht Fröhlich: Galois module structure of algebraic integers, 1983
2 William Fulton: Intersection theory, 1983
3 Jens Carsten Jantzen: Einhüllende Algebren halbeinfacher Lie-Algebren, 1983
4 Wolf Barth, Klaus Hulek Chris Peters, Antonius van de Ven: Compact complex surface, 1984, 2.ª Edição 2004
5 Kurt Strebel: Quadratic differentials, 1984
6 Michael Beeson: Foundations of constructive mathematics: metamathematical studies, 1985
7 Allan Pinkus: n-widths in approximation theory, 1986
8 Ricardo Mañé: Ergodic theory and differentiable dynamics 1987
9 Mikhael Gromov: Partial differential relations, 1986
10 Arthur Besse: Einstein manifolds, 1987
11 Michael D. Fried, Moshe Jarden: Field arithmetic, 1986
12 Jacek Bochnak, Michel Coste, Marie-Françoise Roy: Géométrie algébrique réelle, 1987
13 Eberhard Freitag, Reinhardt Kiehl: Etale cohomology and the Weil conjecture 1988
14 Mark Goresky, Robert MacPherson: Stratified Morse Theory, 1988
15 Tadao Oda: Convex bodies and algebraic geometry: an introduction to the theory of toric varieties, 1988
16 Gerard van der Geer: Hilbert modular surfaces, 1988
17 Grigory Margulis: Discrete subgroups of semisimple Lie groups, 1991
18 Andries Brouwer, Arjeh Cohen, Arnold Neumaier: Distance-regular graphs, 1989
19 Ivar Ekeland: Convexity methods in Hamiltonian mechanics, 1990
20 Alexei Kostrikin: Around Burnside, 1990
21 Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud: Néron models, 1990
22 Gerd Faltings, Ching-Li Chai: Degeneration of abelian varieties, 1990
23 Michel Ledoux, Michel Talagrand: Probability in Banach spaces: isoperimetry and processes, 1991, 2. Auflage 2010
24 Vladimir F. Lazutkin: KAM theory and semiclassical approximations to eigenfunctions, 1993
25 Welington de Melo, Sebastian van Strien: One-dimensional dynamics, 1993
26 Seppo Rickman: Quasiregular mappings, 1993
27 Robert Friedman, John Willard Morgan: Smooth four-manifolds and complex surfaces, 1994
28 Victor Havin, Burglind Jöricke: The uncertainty principle in harmonic analysis, 1993
29 Anthony Joseph: Quantum groups and their primitive ideals, 1995
30 Eckart Viehweg: Quasi-projective moduli for polarized manifolds, 1995
31 Waleri Kozlow: Symmetries, topology and resonances in Hamiltonian mechanics
32 János Kollár: Rational curves on algebraic varieties, 1996
33 Carlos Andrada, Ludwig Bröcker, Jesús M. Ruiz: Constructible sets in real geometry, 1996
34 David Goss: Basic structures of function field arithmetic, 1996
35 Michael Struwe: Variational methods: applications to nonlinear partial differential equations and Hamiltonian systems, 3. Auflage 2000
36 Jacek Bochnak, Michel Coste, Marie-Francoise Roy: Real algebraic geometry, 1998
37 Mariano Giaquinta, Giuseppe Modica, Jiří Souček: Cartesian currents in the calculus of variations 1, 1998
38 Mariano Giaquinta, Giuseppe Modica, Jiří Souček: Cartesian currents in the calculus of variations 2:Variational integrals, 1998
39 Gérard Laumon, Laurent Moret-Bailly: Champs algébriques, 2000
40 Luis Ribes, Pavel Zalesskii: Profinite groups, 2000, 2. Auflage 2010
41 Igor Nikolaev: Foliations on surfaces, 2001
42 Reinhardt Kiehl, Rainer Weissauer: Weil conjectures, perverse sheaves and l'adic Fourier transform, 2001
43 George Greaves: Sieves in number theory, 2001
44 Wolfgang Lück: L2-invariants: theory and applications to geometry and K-theory, 2002
45 Thomas Kappeler, Jürgen Pöschel: KdV & KAM, 2003
46 Michel Talagrand: Spin glasses: a challenge for mathematicians ; cavity and mean field models, 2003
47 Mark Adler, Pierre van Moerbeke, Pol Vanhaecke: Algebraic integrability, Painlevé geometry and Lie algebras, 2004
48, 49 Robert Lazarsfeld: Positivity in algebraic geometry, Teil 1,2, 2004
50 Sergey Neshveyev, Erling Størmer: Dynamic entropy in operator algebras, 2006
51 Boris Khesin, Robert Wendt: The geometry of infinite-dimensional groups, 2009
52 Chris Peters, Joseph Steenbrink: Mixed Hodge Structures, 2009
53 Vítor Araújo, Maria José Pacifico: Three-dimensional flows, 2010
54,55 Michel Talagrand: Mean field models for spin glasses, Teil 1,2, 2011
56 Franc Forstnerič : Stein manifolds and holomorphic mappings: the homotopy principle in complex analysis, 2011, 2. Auflage 2017
57 Francis Buekenhout, Arjeh Cohen: Diagram geometry: related to classical groups and buildings, 2013
58 Eckhard Meinrenken: Clifford algebras and Lie theory, 2013
59 Frédéric Paugam: Towards the mathematics of quantum field theory, 2014
60 Michel Talagrand: Upper and lower bounds for stochastic processes: modern methods and classical problems, 2014
61 Werner Lütkebohmert: Rigid geometry of curves and their Jacobians, 2016
62 Yves Benoist, Jean-François Quint: Random walks on reductive groups, 2016
63 Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis: Analysis in Banach spaces, Volume 1: Martingales and Littlewood-Paley theory, 2016
64 Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer: Information Geometry, 2016
65 Annette Huber-Klawitter, Stefan Müller-Stach: Periods and Nori motives, 2017 (com contribuições de Benjamin Friedrich, Jonas von Wangeheim)
66 Luis Ribes: Profinite graphs and groups, 2017