Publications

Research Articles

(115) The Liouville property for harmonic functions on groups and hypergroups
Methods of Functional Analysis and Topology Vol.23, No.1, 28 pages (2017), pp. 3-15

(114) Hypergroups related to a pair of compact hypergroups (with S. Kawakami, T. Tsurii and S.Yamanaka)
Symmetry, Integrability and Geometry: Methods and Applications 12 2016 III (17 pages)
arXiv: 1605.07010

(113) Commutative hypergroups associated with a hyperfield (with S. Kawakami, T. Tsurii and S.Yamanaka)
Infinite Dimensional Analysis, Quantum Probability and related Topics
arXiv: 160404361 v 1 [math. FA] 15 April 2016

(112) Hypergroups arising from characters of a compact group and its subgroup (with S. Kawakami, T. Tsurii and S. Yamanaka)
to appear in Sci. Math. Japonicae
arXiv: 1605.03744 v 1 [math. RT] 12 May 2016

(111) Hypergroup structures arising from certain dual objects of a hypergroup
(with S. Kawakami)
J. Math. Soc. Japan Vol.69, No.3 (2017),
1179-1195 doi: 10.2969 [jms] / 06931179

(110) Information functionals with applications to random walk and statistics
Journal of Statistical Theory and Practice Volume 9, Issue 4 (2015),
DOI 10.1080/15598608.2015.1053638

(109) Characters of induced representations of a compact group
(with S. Kawakami and S. Yamanaka)
Monatshefte für Mathematik Vol. 176, No.4 (2015),
DOI 10.1007/s00605-015-0749-0

(108) Random fields and hypergroups
In: "Real and Stochastic Analysis.Current Trends" (edited by M.M.Rao),
pp. 85-182, World Scientific 2014

(107) An imprimitivity theorem for representations of a semi-direct product hypergroup (with S.Kawakami)
Journal of Lie Theory Volume 24 No.1 (2014), 159-178

(106) Der Dichter und die Mathematik. Mathematische Anklänge in der Literatur
Manuskript eines am 27.Juni 2014 in La Tour-de-Peilz (Schweiz) gehaltenen Vortrags, 18 Seiten

(105) A Bochner-type representation of positive definite mappings on the dual of a compact group
Communications on Stochastic Analysis Vol.7, No 3 (2013), 459-479

(104) Gedankliche Strenge und begriffliche Schaerfe. Annaeherungen and die Sprache desMathematikers
to appear in „Weltprogammierung“. Max Bense zum 100. Geburtstag, Stuttgart 2013, 23 pages

(103) Quod erat demonstrandum. Erfindung und Rechtfertigung in der Mathematik
Manuscript 2012, 18 pages

(102) Infinite dimensional stationary random fields over an Abelian locally compact group
(with M.M.Rao)
International Journal of Math. Vol 23, No 4 (2012), 1250029, 23 pages

(101) A cohomology approach to the extension problem for commutative hypergroups (with S.Kawakami)
Semigroup Forum Vol.83, No 1 (2011), 371-394

(100) Martingale characterizations of increments processes in a commutative hypergroup (with G. Pap)
Adv.Pure Appl. Math.Vol.1 (2010), 117-140

(99) Positive and negative definite functions on a hypergroup and its dual.
In: Proceedings of the 4th German-Japanese Symposium
“Infinite Dimensional Harmonic Analysis”, Tokyo 2007, pp. 63-96
World Scientific 2008

(98) The truncation inequality for measures on a locally compact Abelian group
(with G. Pap)
Mathematical Inequalities and Applications Vol. 11, No. 3 (2008), 483-49

(97) Polynomial hypergroup structures and applications to probability theory
with (W. R. Bloom)
Publ. Math. Debrecen 72/1-2 (2008), 199-2253

(96) Extensions of Pontryagin hypergroups
(with S. Kawakami)
Probability and Mathematical Statistics Vol. 26, Fasc. 2 (2007), 245 - 260

(95) Extensions of finite commutative hypergroups
(with Y. Katayama, S. Kawakami, K.Kawaski)
Scientiae Mathematicae Japonicae , 65, No.3 (2007), 373-385; e-2007-10, 127-139

(94) Hypergruppen in Analysis und Wahrscheinlichkeitstheorie
Ein Tribut an den Meister
Austrian Journal of Statistics, Volume 34 (2006), Number 4, 411 – 419

(93) On the Lévy-Khintchine decomposition of conditionally positive definite functions
Periodica Mathematica Hungarica Vol. 52 (1), 2006, 19 – 40

(92) Finite commutative hypergroups associated with actions of finite Abelian groups (with T. Jimbo, S. Kawakami, K. Kawasaki)
Bull. Nara Univ. Educ. Vol. 54, No. 2 (Nat.) 2005, 22 – 29

(91) Stationary random fields over graphs and related structures
In: Operator Theory: Advances and Applications, Vol 167, 157 – 171, 2006
Birkhäuser-Verlag Basel/Switzerland

(90) Order relations for linear models: A survey on recent developments
Statistical Papers 47, 331 – 372 (2006)

(89) Paul Lévy’s continuity theorem: some history and recent progress
(with S. Kawakami)
Bull. Nara Univ. Educ. Vol. 54, No. 2 (Nat.) 2005, 11 - 21

(88) Infinite divisibility and embedding of probability measures on a locally compact Abelian group (with Gyula Pap)
In: Infinite Dimensional Harmonic Analysis, Proceedings of the Third Japanese – German Symposium, Tübingen 2003, pp. 99 – 118
World Scientific, New Jersey – London – Singapore – Beijing –Shanghai- Hongkong –Taipei - Chennai 2005

(87) Gaussian hemigroups on a locally compact group (with G. Pap)
Acta Mathematica Hungarica, 103 (3), 2004, 197 – 224

(86) Heinz Bauer – Wissenschaftlicher Weg und Werk
Eine anlässlich des Gedenk – Kolloquiums am 31. Januar 2003 in Erlangen gehaltene Rede
Jahresbericht der DMV 105. Band (2003), Heft 2, 63 – 78

(85) Nicolas Bourbaki und die Axiomatik der Strukturen. Bemerkungen zur Architektur der Mathematik
In: Collection of Papers Dedicated to Professor Dr. Dieter Pumplün by Friends and Colleagues on the Occasion of a Triple Prime Birthday (herausgegeben von Aloys Krieg und Sebastian Walcher), pp. 130 - 142
Lehrstuhl A für Mathematik, RWTH Aachen 2002 / 2003

(84) Martingale characterizations of stochastic processes with independent increments in a locally compact group (with G.Pap)
In: Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 6, No. 4 (2003), 563 – 595

(83) On diffusion hemigroups of probability measures on an abelian locally compact group (with M. S. Bingham)
Result. Math. 37 (2000), 204 – 225

(82) Functional central limit theorems for locally compact groups: the use of infinite dimensional Fourier analysis
In: Infinite Dimensional Harmonic Analysis, Transactions of a Japanese – German Symposium, Kyoto 1999, pp. 143 – 159
D. + M. Gräbner – Verlag, Altendorf 2000

(81) The covariance distribution of a generalized random field over a commutative hypergroup
In: Probability on Algebraic Structures (edited by G. Budzban, PH. Feinsilver, A.
Mukherjea), pp. 73 – 82
Contemporary Mathematics Vol. 261, American Mathematical Society,
Providence, Rhode Island 2000

(80) Convergence of evolution operator families and its applications to functional limit theorems (with G. Pap)
Publicationes Mathematicae Debrecen 58 (2001), 157 – 191

(79) An application of Sobolev spaces for commutative hypergroups (with W. R. Bloom)
In: Trends in Contemporary Infinite Dimensional Analysis and Quantum Probability, Essays in Honor of Professor Takeyuki Hida for his 70 th Birthday (edited by Luigi Accardi, Hui – Hsiung Kuo, Nobuaki Obata, Kimiaki Saito, Si Si, Ludwig Streit), pp. 81 - 100
Istituto Italiano di Cultura, Kyoto 2000

(78) Convergence of convolution hemigroups on a Moore group (with G. Pap)
In: Proceedings of the Colloquium on “Analysis on infinite – dimensional Lie groups and algebras”, pp. 122 – 144
World Scientific, Singapore – New Jersey – London – Hongkong 1998

(77) Statistical morphisms and some concepts of sufficiency
In: Seminarberichte aus dem Fachbereich Mathematik der FernUniversität Hagen, Band 63, Teil 2 (1998), 275 – 306

(76) Über asymptotisch fehlerfreie Übertragbarkeit von Information
In: signum um signum: Festschrift für E. Walther – Bense zu ihrem 75. Geburtstag, pp. 320 – 334,
Agis – Verlag, Feiburg 1997

(75) Infinite divisible and stable statistical experiments
In: Proceedings of the XVIII International Seminar on Stability Problems for Stochastic Models, Debrecen (1997)
Journal of Mathematical Sciences Vol. 93, № 4 (1999), 543 – 551

(74) Convolution hemigroups of bounded variation on a Lie projective group (with G. Pap)
J. London Math. Soc. 59 (1999), 369 – 384

(73) Champs aléatoires généralisés sur les groupes localement compacts abéliens
Math.-Recherches et Applications Vol. 1, № 1 (1999), 51 – 67

(72) Convergence of noncommutative triangular systems of probability measures on a Lie group (with G. Pap)
Journal of Theoretical Probability 10 (1997), 1003 – 1052

(71) Harmonic Analysis on the Disk Hypergroup
2 nd (extended) Edition (with S. Koshi)
Tokyo Metropolitan University 1996

(70) Generation and representation of convolution hemigroups on a polish group
In: Infinite Dimensional Harmonic Analysis, Transcations of a German – Japanese Symposium, Tübingen (1995), pp. 32 – 85
Verlag D. + M. Gräbner, Bamberg 1996

(69) On the generating functional of a convolution semigroup on a Hilbert – Lie group (with E. Coşcun)
Annales Mathématiques Blaise Pascal Vol. 3, № 1 (1996), 51 - 64

(68) Large deviation principles for Markov chains on some compact hypergroups
(with J. Feng)
In: Probability Measures on Groups and Related Structures XI,
Proceedings of a Conference at Oberwolfach, Germany (edited by H. Heyer),
pp. 126 – 140
World Scientific Singapore – New Jersey – London – Hongkong 1995

(67) Generation and representation of continuous convolution families on topological groups
In: Dynamical Systems and Chaos, Proceedings of the International Conference,
Vol. I (edited by N. Aoki, K. Shiraiwa, Y. Takahashi), pp. 72 - 80
World Scientific Singapore – New Jersey – London – Hongkong 1995

(66) Progress in the theory of probability on hypergroups
Contemporary Mathematics Vol. 183 (1995), 191 – 212

(65) Negative definite functions on a commutative hypergroup (with W. R. Bloom)
Probability and Mathematical Statistics Vol. 16, № 1 (1995), 157 - 177

(64) On an extended notion of common conditional probability (with S. Yamada) Probability and Mathematical Statistics Vol. 15 (1995), 353 – 363

(63) Harmonic Analysis on the Disk Hypergroup (with S. Koshi)
Mathematical Seminar Notes, Tokyo Metropolitan University 1993

(62) Functional limit theorems for random walks on one – dimensional hypergroups
In: Proceedings “Stability Problems for Stochastic Models”,
(edited by V. V. Kalashnikov and V. M. Zolotarev), pp. 45 – 57
Lectures Notes in Math. Vol. 1546, Springer 1993

(61) Measures of finite energy on a commutative hypergroup (with Y. Wang)
Rendiconti del Seminario Mathematico & Fisico di Milano
Vol. LIX (1989), 2/ 1992, 245 - 267

(60) Positive definite functions and the Lévy continuity theorem for commutative hypergroups (with W. R. Bloom and Y. Wang)
In: Probability Measures on Groups X (edited by H. Heyer), pp. 19 - 38
Plenum Publishing Corporation, New York 1992

(59) Preservation of classical sufficiency
Jour. Math. Phys. Sci. Vol. 25, № 5 & 6, (1991), 613 - 633

(58) Some remarks on weak sufficiency (with T. Kusama)
Statistical Papers 32 (1991), 137 – 154

(57) Stationary random fields over hypergroups
In: Gaussian Random Fields (edited by K. Ito and T. Hida), pp. 197 – 213
World Scientific Publishers, Singapore – New Jersey – London – Hongkong 1991

(56) Locally compact groups: Origin, analysis, and applications
In: Functional Analysis and Related Topics (edited by S. Koshi), pp. 1 – 18
World Scientific Publishers, Singapore – New Jersey – London – Hongkong 1991

(55) Fraktale: Mathematische Definition und ästhetische Signifikanz
In: Festschrift für Max Bense (herausgegeben von E. Walther und U. Bayer)
pp. 347 – 361
Agis – Verlag Baden – Baden 1990

(54) On local integrability and transience of convolution semigroups of measures (with G. Turnwald)
Acta Applicandae Mathematicae 18 (1990), 283 – 296

(53) Convolution semigroups and potential kernels on a commutative hypergroup
In: The Analytic and Topological Theory of Semigroups
(edited by K. H. Hofmann; Jimmie D. Lawson; John S. Pym), pp. 279 – 312
DeGruyter Expositions in Mathematics 1 (1990)

(52) Das Einbettungsproblem der Wahrscheinlichkeitstheorie
Leopold Schmetterers Beiträge zur strukturellen Wahrscheinlichkeitstheorie und neuere Entwicklungen
Österr. Zeitschrift für Statistik und Informatik, 19 Jg., Heft 2, (1989), 191 – 213

(51) Convolution semigroups of local type on a commutative hypergroup
Hokkaido Math. J. 18 (1989), 321 – 337

(50) Characterisation of potential kernels of transient convolution semigroups on a commutative hypergroup
In: Probability Measures on Groups IX (edited by H. Heyer), pp. 21 – 35
Lectures Notes in Math. Vol. 1379, Springer 1989

(49) Infinitely divisible probability measures on a discrete Gelfand pair
Nagoya Math. J. 116 (1989), 43 – 62

(48) Bemerkungen über den Vergleich linearer normaler Experimente
Monatshefte für Mathematik 106 (1988), 9 – 23

(47) Continuity of convolution semigroups on hypergroups (with W. R. Bloom)
Journal of Theoretical Probability Vol. 1, № 3 (1988), 271 – 286

(46) Convergence of Markov chains on a homogeneous tree
Probability Seminar of the Japan Mathematical Society 1988

(45) Bayesian aspects in the theory of comparison of statistrical experiments
In: Probability and Bayesian Statistics (edited by R. Viertl),
pp. 247 – 256
Plenum Press New York and London 1987

(44) Non – symmetric translation invariant Dirichlet forms on hypergroups (with W. R. Bloom)
Bull. Austral. Math. Soc. Vol. 36 (1987), 61 – 72

(43) Generalized translation structures and invariant Feller semigroups
In: Mathematical Statistics and Probability Theory Vol. A
(edited by M. L. Puri, P. Révész, W. Wertz), pp. 143 – 194
D. Reidel Publishing Company Dordrecht, Boston, Lancaster, Tokyo 1987

(42) Convolution semigroups on a Sturm - Liouville structure
Symposia Mathematica, Istituto Nazionale di Alta Matematica, Roma,
Vol. XXIX (1987), 131 - 162

(41) Recent contributions to the embedding problem for probability measures on locally compact groups
J. Multivariate Analysis Vol. 19, № 1 (1986), 119 - 131

(40) Distributions dissipatives et semigroupes de convolution des measures sur un groupe localement compact
In: Probabilités sur les Structures Géométrique, pp. 87 – 99,
Actes des Journées de Toulouse (18 – 22 juin 1984), Publications du Laboratoire de Statistique et Probabilités № 1 – 85, Université Paul Sabatier, Toulouse 1985

(39) Convolution semigroups and resolvent families of measures on hypergroups (with W. R. Bloom)
Math. Z. 188 (1985), 449 – 474

(38) Probability theory on hypergroups: a survey
In: Probability Measures on Groups,
Proceedings of the 7 th Oberwolfach Conference, pp. 481 – 550.
Springer Lecture Notes in Mathematics Vol. 1064 (1983)

(37) Transient Feller semigroups on certain Gelfand pairs
Bulletin of the Institute of Mathematics, Academia Sinica, Vol. II, № 2 (1983),
227 – 256

(36) Convolution semigroups of probability measures on Gelfand pairs
Expo. Math. 1 (1983), 3 - 45

(35) Structural aspects in the theory of random walk
Journal of the Korean Statistical Society Vol. II; № 2 (1982), 118 – 130

(34) Convergence of convolution products of probability measures on a hypergroup (with W. R. Bloom)
Rendiconti di Mathematica (3) 1982, Vol. 2, Serie VII, 547 – 563

(33) The Fourier transform of probability measures on a hypergroup (with W. R. Bloom)
Rendiconti di Mathematica (2) 1982, Vol. 2, Serie VII, 315 – 334

(32) An application of the method of moments to the central limit therorem on hyperbolic spaces
In: Analytic Methods in Probability Theory, Proceedings Oberwolfach 1980,
Lecture Notes in Mathematics Vol. 861, 65 – 73 (1981)

(31) Moments of probability measures on a group
Internat. J. Math. & Math. Sci. 4 (1981), 1 - 37

(30) Information measures and sufficiency
Symposia Mathematica, Istituto Nazionale di Alta Matematica, Roma,
Vol. XXV (1980), 25 – 54

(29) Stetige Hemigruppen von Wahrscheinlichkeitsmaßen und additive Prozesse auf einer lokalkompakten Gruppe
Nieuw Archief voor Wiskunde (3), XXVII (1979), 287 – 340

(28) Invariante Markoff - Kerne und der Vergleich von Translationsexperimenten
Monatshefte für Mathematik 88 (1979), 123 – 135

(27) Semi – groups de convolution sur un groupe localement compact et applications à la théorie des probabilités
In: Ecole d’Eté de Probabilités, de Saint – Flour VII – 1977,
Lecture Notes in Mathematics Vol. 678, 173 – 236, Springer – Verlag (1978)

(26) Probability measures on almost periodic groups
Symposia Mathematica, Istituto Nazionale di Alta Matematica, Roma,
Vol. XXI (1977); 281 – 311

(25) Gauss distributions and central limit theorem for locally compact groups
Colloquia Mathematica Societatis János Bolyai, 11: Limit Theorems of Probability Theory (1975), 105 – 134

(24) Probabilistic characterization of certain classes of locally compact groups
Symposia Mathematica, Istituto Nazionale di Alta Matematica, Roma,
Vol. XVI (1975), 315 – 355

(23) The embedding of probability measures on a locally compact group
In: Atas do 9o Colóquio Brasileiro de Matemática, 377 – 395.
Poços de Caldas, 9 a 28 di jullio de 1973

(22) Groups with Chu Duality
In: Probability and Information Theory II (ed. by M. Behara, K. Krickeberg and J. Wolfowitz), 181 – 215,
Lecture Notes in Mathematics Vol. 296, Springer – Verlag (1973)

(21) Gaußsche Wahrscheinlichkeitsmaße auf Corwinschen Gruppen (mit Chr. Rall)
Math. Zeitschrift 128 (1972), 343 - 361

(20) Maßtheoretische Ergänzungen zur Risikotheorie
(Struktur des Risikoprozesses)
Blätter der Deutschen Gesellschaft für Versicherungsmathematik X (1972), 451 – 465

(19) Infinitely divisible probability measures on compact groups
Lectures delivered at Tulane University, New Orleans,
Lecture Notes in Mathematics Vol. 247, Springer (1972), 55 – 249

(18) The duality principle and applications to probability theory on locally compact groups Papers from the „Open House for Probabilists“,
Matematisk Institut, Aarhus Universitet,
Various Publication Series № 21 (1972), 118 - 128

(17) A central limit theorem for compact Lie groups
Papers from the „Open House for Probabilists“,
Matematisk Institut, Aarhus Universitet,
Various Publication Series № 21 (1972), 101 – 117

(16) Zum Erschöpftheitsbegriff von D. Blackwell
Metrika Bd. 19, Heft 1 (1972), 54 – 67

(15) Remarques sur une axiomatique de la variance
Colloques Internationaux du Centre National de la Recherche Scientifique, № 186 (1970), 177 – 189

(14) Sur la divisibilité des probabilités dans un groupe topologique (mit A. Tortrat)
Z. Wahrscheinlichkeitstheorie verw. Geb. 16 (1970), 307 – 320

(13) Erschöpftheit und Invarianz beim Vergleich von Experimenten
Z. Wahrscheinlichkeitstheorie verw. Geb. 12 (1969), 21 – 55

(12) Das Äquivalenzprinzip der Wahrscheinlichkeitstheorie für lokalkompakte Gruppen und homogene Räume
Sitzungsberichte der Bayer. Akad. Wiss. Math. – Nat. Kl. (1968), 1 – 11

(11) L’analyse de Fourier non – commutative et applications à la théorie des probabilités
Ann. de l’Institut H. Poincaré Vol. IV, № 2 (1968), 143 - 164

(10) Allgemeine Grenzwertsätze der Wahrscheinlichkeitsrechung
Studies in Mathematical Statistics: Theory and Applications,
Budapest (1968), 57 – 73

(9) Fourier transforms and probabilities on locally compact groups
Jahresberichte der Deutschen Mathematiker – Vereinigung Bd. 70,
Heft 3 (1968), 109 – 147

(8) Factorization of probability measures on locally compact groups
Z. Wahrscheinlichkeitstheorie verw. Geb. 8 (1967), 231 – 258

(7) On the convergence principle of B. M. Kloss
Math. Scand. 19 (1966), 211 – 216

(6) Drei Wege zu den Grundbegriffen der Differentialrechnung
Math. Phys. Sem. Ber. XIII (1966), 202 – 215

(5) Über Haarsche Maße auf lokalkompakten Gruppen
Archiv der Mathematik Vol. XVII (1966), 347 – 351

(4) Lineare Algebra und ihre Anwendungen auf die analytische Geometrie, I, II, III Mathematisch - Naturwissenschaftlicher Unterricht Bd. 18, Hefte 10 - 12 (1965 / 1966), 353 – 360, 392 – 400, 448 - 458

(3) Mathematische Methoden der Untenehmensforschung
Mathematisch – Naturwissenschaftlicher Unterricht Bd. 17, Heft 6 (1964), 241 – 247

(2) Neuere Ergebnisse aus der Theorie der Wahrscheinlichkeitsmaße auf lokalkompakten und Lieschen Gruppen
Transactions of the 3 rd Prague Conference on Information Theory,
Statistical Decision Functions, Random Processes
(1964), 277 - 284

(1) Untersuchungen zur Theorie der Wahrscheinlichkeitsverteilungen auf lokalkompakten Gruppen
Privatdruck, Dissertation Hamburg (1963), 67 Seiten
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