• Title, Summary, Keyword: unitary group

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EISENSTEIN SERIES WITH NON-UNITARY TWISTS

  • Deitmar, Anton;Monheim, Frank
    • Journal of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.507-530
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    • 2018
  • It is shown that for a non-unitary twist of a Fuchsian group, which is unitary at the cusps, Eisenstein series converge in some half-plane. It is shown that invariant integral operators provide a spectral decomposition of the space of cusp forms and that Eisenstein series admit a meromorphic continuation.

INTERVAL-VALUED FUZZY GROUP CONGRUENCES

  • Lee, Jeong Gon;Hur, Kul;Lim, Pyung Ki
    • Honam Mathematical Journal
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    • v.38 no.2
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    • pp.403-423
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    • 2016
  • We introduce the concepts of interval-valued fuzzy complete inner-unitary subsemigroups and interval-valued fuzzy group congruences on a semigroup. And we investigate some of their properties. Also, we prove that there is a one to one correspondence between the interval-valued fuzzy complete inner-unitary subsemigroups and the interval-valued fuzzy group congruences on a regular semigroups.

DILATION OF PROJECTIVE ISOMETRIC REPRESENTATION ASSOCIATED WITH UNITARY MULTIPLIER

  • Im, Man Kyu;Ji, Un Cig;Kim, Young Yi;Park, Su Hyung
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.4
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    • pp.367-373
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    • 2007
  • For a unital *-subalgebra of the space $\mathcal{L}^a(X)$ of all adjointable maps on a Hilbert $\mathcal{B}$-module X with a $C^*$-algebra $\mathcal{B}$, we study unitary operator (in such algebra)-valued multiplier ${\sigma}$ on a normal, generating subsemigroup S of a group G with its extension to G. A dilation of a projective isometric ${\sigma}$-representation of S is established as a projective unitary ${\rho}$-representation of G for a suitable unitary operator (in some algebra)-valued multiplier ${\rho}$ associated with the multiplier ${\sigma}$ which is explicitly constructed.

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A GENERALIZATION OF STONE'S THEOREM IN HILBERT $C^*$-MODULES

  • Amyari, Maryam;Chakoshi, Mahnaz
    • The Pure and Applied Mathematics
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    • v.18 no.1
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    • pp.31-39
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    • 2011
  • Stone's theorem states that "A bounded linear operator A is infinitesimal generator of a $C_0$-group of unitary operators on a Hilbert space H if and only if iA is self adjoint". In this paper we establish a generalization of Stone's theorem in the framework of Hilbert $C^*$-modules.

UNITARY SERIES OF $GL_2(R)$ AND $GL_2(C)$

  • Kim, Seon-Ja
    • Communications of the Korean Mathematical Society
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    • v.9 no.3
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    • pp.521-529
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    • 1994
  • This paper studies the realization of irreducible unitary representations of $GL_2(R)$ and $GL_2(C)$ by Bargmann's classification[1]. Since the representations of general matrix groups can be obtained by the extensions of characters of a special linear group, we shall follow to a large extent the pattern of the results in [5], [6], and [8]. This article is divided into two sections. In the first section we describe the realization of principal series and discrete series and complementary series of $GL_2(R)$. The last section is devoted to the derivation of principal series and complementary series of $GL_2(C).

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A NOTE ON THE COMPLEXIFICATION OF CONFORMAL GROUP II*

  • Lee, Ke-Seung
    • Journal of the Chungcheong Mathematical Society
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    • v.8 no.1
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    • pp.137-145
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    • 1995
  • In the white noise analysis the one-parameter groups play the powerful role. In this report, we will see a subgroup of infinite dimensional unitary group $U_{\infty}$ including guage transform and structure of this subgroup under the view point of Lie algebra.

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