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122 P.E.T. JØRGENSEN, D.P. PROSKURIN, AND YU.S. SAMO ĬLENKO Unbounded representations of Wick algebras will be considered in more detail later. Acknowledgements. Yu. Samoĭlenko and Dan. Proskurin express their gratitude to Prof. Vasyl L. Ostrovskyĭ and Stanislav Popovych for their attention and helpful discussions. We also thank Brian Treadway for proofreading and polishing. References [1] N. Bourbaki, Eléments de mathematique, Fasc. XXXIV: Groupes et algebres de Lie, Chap. 4, 5, 6, Hermann, Paris, 1968. [2] M. Bo˙zejko and R. Speicher, Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces, Math. Ann., 300 (1994), 97-120. [3] K. Dykema and A. Nica, On the Fock representation of the q-commutation relations, J. Reine Angew. Math., 440 (1993), 201-212. [4] O.W. Greenberg, Particles with small violations of Fermi or Bose statistics, Phys. Rev. D (3), 43 (1991), 4111-4120. [5] P.E.T Jørgensen, L.M. Schmitt and R.F. Werner, q-canonical commutation relations and stability of the Cuntz algebra, Pacific J. Math., 165(1) (1994), 131-151. [6] P.E.T. Jørgensen, L.M. Schmitt, and R.F. Werner, Positive representations of general commutation relations allowing Wick ordering, J. Funct. Anal., 134 (1995), 33-99. [7] E.C. Lance, Finitely-presented C ∗ -algebras, Operator Algebras and Applications, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 495, Kluwer Acad. Publ., Dordrecht, 1997, 255-266. [8] V. Ostrovskyĭ and Yu. Samoĭlenko, Introduction to the Theory of Representations of Finitely Presented ∗-Algebras, I: Representations by Bounded Operators, The Gordon and Breach Publishing Group, London, 1999. [9] D. Proskurin, Homogeneous ideals in Wick ∗-algebras, Proc. Amer. Math. Soc., 126(11) (1998), 3371-3376. [10] W. Pusz and S.L. Woronowicz, Twisted second quantization, Rep. Math. Phys., 27 (1989), 231-257. [11] K. Schmüdgen, Unbounded Operator Algebras and Representation Theory, Operator Theory: Advances and Applications, Vol. 37, Birkhäuser, Basel, 1990. Received May 25, 1999. The first author was partially supported by NSF grant no. DMS- 9700130. The third author was partially supported by CRDF grant no. UM1-311 Department of Mathematics The University of Iowa Iowa City, Iowa 52242-1419 E-mail address: jorgen@math.uiowa.edu Institute of Mathematics Ukrainian National Academy of Sciences Tereshchinkivs’ka, 3 Kiev, 252601 Ukraine
E-mail address: prosk@imath.kiev.ua BRAIDED OPERATOR COMMUTATORS 123 Institute of Mathematics Ukrainian National Academy of Sciences Tereshchinkivs’ka, 3 Kiev, 252601 Ukraine E-mail address: Yurii Sam@imath.kiev.ua
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Pacific Journal of Mathematics Volu
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PACIFIC JOURNAL OF MATHEMATICS Vol.
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EIGENVALUES ASYMPTOTICS 3 (i) If pm
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EIGENVALUES ASYMPTOTICS 5 Corollary
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Thus, by the Itô formula, we have
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Therefore, K1(t) ≡ t 2−d/2 ≤
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EIGENVALUES ASYMPTOTICS 11 The chan
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EIGENVALUES ASYMPTOTICS 13 Here Res
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IMAGINARY QUADRATIC FIELDS 17 Table
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IMAGINARY QUADRATIC FIELDS 19 and t
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IMAGINARY QUADRATIC FIELDS 21 Propo
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〈σ 〈σ〉 〈σ, τ〉 2 〈1
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IMAGINARY QUADRATIC FIELDS 25 Then
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IMAGINARY QUADRATIC FIELDS 27 were
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IMAGINARY QUADRATIC FIELDS 29 Thus
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IMAGINARY QUADRATIC FIELDS 31 [3] ,
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34 CARINA BOYALLIAN spherical serie
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36 CARINA BOYALLIAN Here I G MAN (
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38 CARINA BOYALLIAN where k ≤ [ n
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40 CARINA BOYALLIAN The case G = Sp
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42 CARINA BOYALLIAN we can, since i
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44 CARINA BOYALLIAN and this formul
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46 CARINA BOYALLIAN Here, J(ν) int
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48 CARINA BOYALLIAN [V] D. Vogan, R
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50 ROBERT F. BROWN AND HELGA SCHIRM
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Page 74 and 75: 72 ROBERT F. BROWN AND HELGA SCHIRM
Page 84 and 85: 82 GILLES CARRON à l’infini s’
Page 86 and 87: 84 GILLES CARRON isométriques au d
Page 88 and 89: 86 GILLES CARRON Comme D est ellipt
Page 90 and 91: 88 GILLES CARRON Réciproquement si
Page 92 and 93: 90 GILLES CARRON où H est la proje
Page 94 and 95: 92 GILLES CARRON 2.a. Exemples repo
Page 96 and 97: 94 GILLES CARRON alors si σ ∈ C
Page 98 and 99: 96 GILLES CARRON Ainsi s’il exist
Page 100 and 101: 98 GILLES CARRON Proposition 2.7. N
Page 102 and 103: 100 GILLES CARRON l’espace des 1
Page 104 and 105: 102 GILLES CARRON compact. De même
Page 106 and 107: 104 GILLES CARRON 4. Application du
Page 108 and 109: 106 GILLES CARRON Dans le cas où l
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Page 119 and 120: Then, for 1 < k ≤ m + 1, we have
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Page 128 and 129: 124 DANIEL J. MADDEN times. Further
Page 130 and 131: 126 DANIEL J. MADDEN Further, s t
Page 132 and 133: 128 DANIEL J. MADDEN Now the whole
Page 134 and 135: 130 DANIEL J. MADDEN and β = 1 −
Page 136 and 137: 132 DANIEL J. MADDEN We can simplif
Page 138 and 139: 134 DANIEL J. MADDEN surd, but we n
Page 140 and 141: 136 DANIEL J. MADDEN and d = d(u, v
Page 142 and 143: 138 DANIEL J. MADDEN (6l + 7) k +
Page 144 and 145: 140 DANIEL J. MADDEN Then the conti
Page 146 and 147: 142 DANIEL J. MADDEN Thus n + 1 1 =
Page 148 and 149: 144 DANIEL J. MADDEN If we take b =
Page 150 and 151: 146 DANIEL J. MADDEN b, 2b(2bn + 1)
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TANGLES, 2-HANDLE ADDITIONS AND DEH
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TANGLES, 2-HANDLE ADDITIONS AND DEH
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SOME CHARACTERIZATION, UNIQUENESS A
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and SOME CHARACTERIZATION, UNIQUENE
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SYMPLECTIC SUBMANIFOLDS FROM SURFAC
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208 PAULO TIRAO Theorem. The affine
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210 PAULO TIRAO It follows from the
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212 PAULO TIRAO K ρ1 (0,−1,1) =
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214 PAULO TIRAO Theorem 2.7. Let ρ
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216 PAULO TIRAO Notation: By A = [
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218 PAULO TIRAO Now is not difficul
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220 PAULO TIRAO Regard H n (Z2 ⊕
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222 PAULO TIRAO is an isomorphism.
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224 PAULO TIRAO Lemma 4.2. Let Λ1
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226 PAULO TIRAO (c)1 B1 B2 B3 B1 0
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228 PAULO TIRAO ⎛ ⎜ B2 = ⎜
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230 PAULO TIRAO being those in whic
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232 PAULO TIRAO Hence, if ρ = m1χ
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(1.6) HÖLDER REGULARITY FOR ∂ 23
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HÖLDER REGULARITY FOR ∂ 239 can
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HÖLDER REGULARITY FOR ∂ 241 wher
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HÖLDER REGULARITY FOR ∂ 243 Theo
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Note (4.7) bD∩U ′ i dzA j J H
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HÖLDER REGULARITY FOR ∂ 247 p. 1
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similarly, we can prove HÖLDER REG
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HÖLDER REGULARITY FOR ∂ 251 For
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Now if n1 ≥ 2, l ∈ S1, then (4.
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HÖLDER REGULARITY FOR ∂ 255 Refe
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