Markov Operators on the Solvable Baumslag–Solitar Groups

REFERENCES

• Baum , P. , Connes , A. and Higson , N. 1994 . “Classifying spaces for proper actions and K-theory of group C*-algebras”. ” . In C*-algebras 1943–1993: a fifty year celebration Edited by: Doran , R. S. 241 – 291 . [Baum et al. 1994], Contemp. Math. 167
   Google Scholar
• Baumslag , G. and Solitar , D. 1962 . “Some two-generator one-relator non-hopfian groups” . Bull. Amer. Math. Soc. , 68 : 199 – 201 . [Baumslag and Solitar 1962]
   Web of Science ®Google Scholar
• Béguin , C. , Valette , A. and Zuk , A. 1997 . “On the spectrum of a random walk on the discrete Heisenberg group, and the norm of Harper's operator” . J. Geometry and Physics , 21 : 337 – 356 . [Béguin et al. 1997]
   Web of Science ®Google Scholar
• Béguin , C. , Bettaieb , H. and Valette , A. 1999 . “k-theory for C*-algebras of one-relator groups” . K-Theory , 16 ( 3 ) : 277 – 298 . [Béguin et al. 1999]
   Google Scholar
• Bultheel , A. 1995 . “Learning to swim in a sea of wavelets” . Bull. Belg. Math. Soc. , 2 : 1 – 44 . [Bultheel 1995]
   Google Scholar
• Daubechies , I. 1992 . Ten lectures on wavelets Philadelphia , PA : Society for Industrial and Applied Mathematics (SIAM). . [Daubechies 1992], CBMS/NSF regional conference series in applied mathematics 61
   Google Scholar
• Day , M. M. 1964 . “Convolutions, means and spectra” . Illinois J. Math. , 8 : 100 – 111 . [Day 1964]
   Google Scholar
• Dixmier , J. 1977 . C*-algebras Amsterdam : North Holland. . [Dixmier 1977]
   Google Scholar
• Farb , B. and Mosher , L. 1998 . “A rigidity theorem for the solvable Baumslag-Solitar groups” . Invent. Math. , 131 : 419 – 451 . [Farb and Mosher 1998]
   Web of Science ®Google Scholar
• Halmos , P. R. 1967 . A Hilbert space problem book New York : Van Nostrand. . [Halmos 1967], Reprinted by Springer, 1982
   Google Scholar
• de la Harpe , P. , Robertson , A. G. and Valette , A. 1993 . “On the spectrum of the sum of generators of a finitely generated group” . Israel J. Math. , 81 : 65 – 96 . [de la Harpe et al. 1993]
   Web of Science ®Google Scholar
• de la Harpe , P. , Robertson , A. G. and Valette , A. 1994 . “On the spectrum of the sum of generators of a finitely generated group, II” . Colloquium Math. , 65 : 87 – 102 . [de la Harpe et al. 1994]
   Google Scholar
• Heath-Brown , D. R. 1986 . “Artin's conjecture for primitive roots” . Quart. J. Math. , 37 : 27 – 38 . [Heath-Brown 1986]
   Web of Science ®Google Scholar
• Higson , N. and Kasparov , G. 1997 . “Operator k-theory for groups which act properly and isometrically on Hilbert space” . Electron. Res. Announc. Amer. Math. Soc. , 3 : 131 – 142 . [Higson and Kasparov 1997]
   Google Scholar
• Hooley , C. 1967 . “On Artin's conjecture” . J. reine angew. Math. , 226 : 209 – 220 . [Hooley 1967]
   Google Scholar
• Kasparov , G. G. and Skandalis , G. 1991 . “Groups acting on buildings, operator K-theory, and Novikov's conjecture” . K-theory , 4 : 303 – 337 . [Kasparov and Skandalis 1991]
   Google Scholar
• Kesten , H. 1959 . “Symmetric random walks on groups” . Trans. Amer. Math. Soc. , 92 : 336 – 354 . [Kesten 1959]
   Google Scholar
• Murty , M. R. 1988 . “Artin's conjecture for primitive roots” . Math. Intelligencer , 10 : 59 – 67 . [Murty 1988]
   Web of Science ®Google Scholar
• Pittet , C. and SaloffCoste , L. 1999 . “Amenable groups, isoperimetric profiles and random walks”. ” . In Geometric group theory down under (Canberra, 1996) Edited by: Cossey , J. 293 – 316 . Berlin : de Gruyter. . [Pittet and Saloff-Coste 1999]
   Google Scholar
• Robert , A. 1983 . Introduction to the representation theory of compact and locally compact groups Cambridge : Cambridge Univ. Press. . [Robert 1983], London Math. Soc. Lect. Note Ser. 80
   Google Scholar
• Szwarc , R. 1998 . “Norm estimates of discrete Schrödinger operators” . Coll. Math. , 76 : 153 – 160 . [Szwarc 1998]
   Google Scholar
• Valette , A. 1989 . “The conjecture of idempotents: a survey of the C*-algebraic approach” . Bull. Soc. Math. Belg. , 41 : 485 – 521 . [Valette 1989]
   Google Scholar