This volume contains contributions on recent results in infinite dimensional harmonic analysis and its applications to probability theory. Some papers deal with purely analytic topics such as Frobenius reciprocity, diffeomorphism groups, equivariant fibrations and Harish-Chandra modules. Several other papers touch upon stochastic processes, in particular Levy processes. The majority of the contributions emphasize on the algebraic-topological aspects of the theory by choosing configuration spaces, locally compact groups and hypergroups as their basic structures. The volume provides a useful survey of innovative work pertaining to a highly actual section of modern analysis in its pure and applied shapings.
Author(s): Herbert Heyer
Edition: illustrated edition
Publisher: World Scientific Pub Co (
Year: 2005
Language: English
Pages: 366
CONTENTS......Page 8
Preface......Page 6
Shigoto nakama de ari yujin de atta kare no omoide......Page 10
In Memory of a Colleague and Friend H. Heyer......Page 12
In Memory of Professor Shozo Koshi Y. Takahashi......Page 14
1 Introduction......Page 16
2 De Rham complex over a configuration space......Page 18
3 Von Neumann dimensions of symmetric ten- sor powers of Hilbert spaces......Page 23
4 L2-Betti numbers of configuration spaces of coverings......Page 25
References......Page 28
1. INTRODUCTION ET NOTATIONS......Page 32
2. UN LEMME CLEF......Page 33
3. UNE RECIPROCITE DE FROBENIUS......Page 34
4. EXEMPLES......Page 39
REFERENCES......Page 49
1. Introduction......Page 52
2. Monotone Independence......Page 54
3. Conditional Expectations......Page 58
4. Monotone LQvy Processes......Page 60
5. The Markov Semigroup of a Monotone LQvy Process......Page 65
6.2. Monotone Brownian motion......Page 68
7. Martingales......Page 69
References......Page 71
Introduction......Page 74
1. Metric operator spaces and their duals......Page 75
2. Realizations of stochastic matrices......Page 77
3. Extension of states included......Page 79
References......Page 85
1.1. Finite-dimensional noncommutative case.......Page 86
1.2. Finite-dimensional commutative case.......Page 87
2. NON-COMMUTATIVE LP-SPACES......Page 89
3. STOCHASTIC DIFFERENTIAL EQUATIONS ON L2(M)......Page 90
4. HEAT KERNEL MEASURES......Page 91
5. CAMERON-MARTIN GROUP AND ISOMETRIES.......Page 92
REFERENCES......Page 96
1 M-semigroups, stable hemigroups and self-decomposability......Page 98
2 Remarks on root-compactness and embeddability......Page 101
3 Space-time- and background driving processes......Page 105
References......Page 110
2 Preliminaries......Page 114
3 Gaussian measures......Page 115
5.1 Gaussian measures on Rd......Page 118
5.3 Gaussian measures on T......Page 119
5.4 Gaussian measures on solenoidal groups......Page 120
6 Weakly infinitely divisible measures......Page 121
7 Embedding property......Page 122
8 Gaussian and diffusion hemigroups......Page 126
References......Page 132
Character Formula for Wreath Products of Finite Groups with the Infinite Symmetric Group T. Hirai and E. Hirai......Page 134
1.1. Definition of wreath product G (T)......Page 135
1.2. Standad decomposition and conjugacy classes......Page 136
2. Characters of wreath product group G (T)......Page 137
4. Limits of characters of G (T) as n......Page 140
5. Method of proving Theorem 2.1......Page 141
7. Subgroups and their representations for G (T)......Page 143
8. Increasing sequences of subgroups GN G......Page 144
9. Partial centralization with respect to DJN(T)......Page 145
10. Limits of centralizations......Page 147
11. Criterion for extremality......Page 149
12. Final step of the proof of Theorem 2.1......Page 151
References......Page 153
1. Introduction......Page 156
2.1. Transition measure of a diagram......Page 159
2.2. A trace formula......Page 161
3.1. Biane ’s asymptotic formula......Page 163
3.2. Proof of Biane's formula......Page 164
3.3. Auxiliary estimates......Page 167
4.1. Scheme of concentration phenomenon......Page 169
References......Page 173
1. Introduction......Page 176
2. Notation......Page 177
3. Radial maximal functions......Page 179
4. Real Hardy spaces......Page 181
5. Atomic Hardy spaces......Page 184
6. Characterization of H1 (G//K)......Page 187
References......Page 190
I. Introduction......Page 192
II. Partial Malliavin Calculus......Page 193
III. Bismut-Witten current......Page 195
References......Page 199
1 The problems......Page 202
2 The case for diffusions on tori......Page 204
3 The case for diffusions on Euclidean spaces......Page 205
4 Examples......Page 208
References......Page 209
Introduction......Page 212
1.1. Special linear group......Page 215
1.3. Quadratic space......Page 216
2. Equivariant double fibration......Page 217
3. Double fibration related to the natural representations......Page 220
3.1. Tensor products......Page 221
3.2. Contraction by the action of a general linear group......Page 222
4.1. Resolution via the contmction by the action of GL(n, C)......Page 224
4.2. Resolution via the action of the orthogonal and symplectic groups......Page 226
References......Page 227
1. Introduction......Page 228
2.1. Underlying Gelfand rriple......Page 230
2.2. Hida-Kubo-Takenaka Space......Page 232
2.3. White Noise Operators......Page 233
2.4. Gaussian Realization......Page 234
3.2. Admissible White Noise Operators......Page 235
3.3. Admissible White Noise Opemtors with Supporter......Page 237
4.1. lhnslation Opemtor......Page 238
4.2. Gross Derivative......Page 239
4.3. Annihilation- and Creation- Derivatives......Page 241
4.4. Fock Expansion of an Admissible Opemtor......Page 243
4.6. Pointwise QWN-Derivatives......Page 245
References......Page 246
1. Introduction......Page 248
2.1. The finite dimensional case......Page 249
2.2. The infinite dimensional case......Page 253
3. Infinitesimally invariance implies Gibbsian......Page 256
4. Application......Page 257
References......Page 260
1. Introduction......Page 264
2. Deformations of commutative hypergroups......Page 265
3. Deformation of convolution semigroups......Page 270
References......Page 278
Introduction......Page 280
1 Functionals of Gaussian noise and Poisson noise......Page 281
2 The Levy Laplacian acting on multiple Wiener integrals......Page 283
3 The Levy Laplacian acting on WNF-valued functions......Page 285
4 An infinite dimensional stochastic process associated with the Levy Laplacian......Page 286
References......Page 289
Levy Processes on Deformations of Hopf Algebras M. Schurmann......Page 292
References......Page 302
1. Introduction......Page 304
2.1. Restricted product measure with infinite mass......Page 306
2.2 Action of Diff0(M) from the left and of G from the right......Page 308
2.3 Representation space H( )......Page 309
3. Irreducibility......Page 312
4. Equivalence......Page 313
References......Page 325
An Application of the Method of Moments in Random Matrix Theory M. Stolz......Page 328
1. Moments and Weak Convergence......Page 329
2. Application to Random Matrices......Page 333
References......Page 339
1. Introduction......Page 340
2.1. Associated cycle and isotropy repwsentation......Page 342
2.2. Induced module r(Z)......Page 345
2.3. Homomorphism T = T(j)......Page 346
2.4. IIrreducibility......Page 347
2.5. Case of unitary highest weight representations......Page 348
3. Utility of the dual (S(g), Kc)-module......Page 349
3.1. Kc-finite dual M* and its submodule......Page 350
3.2. A suflcient condition for I = Anns(g)M......Page 352
3.3. Difleerential opemtor of gmdient type......Page 353
4.1. Discrete series......Page 356
4.2. Results of Hotta-Parthasamthy......Page 357
4.3. Description of associated cycle......Page 359
4.4. Submodule U (Qc)......Page 360
4.5. Relation to the Richardson orbit......Page 361
References......Page 364
