• 제목/요약/키워드: convolution algebra

검색결과 26건 처리시간 0.024초

APPROXIMATE IDENTITY OF CONVOLUTION BANACH ALGEBRAS

  • Han, Hyuk
    • 충청수학회지
    • /
    • 제33권4호
    • /
    • pp.497-504
    • /
    • 2020
  • A weight ω on the positive half real line [0, ∞) is a positive continuous function such that ω(s + t) ≤ ω(s)ω(t), for all s, t ∈ [0, ∞), and ω(0) = 1. The weighted convolution Banach algebra L1(ω) is the algebra of all equivalence classes of Lebesgue measurable functions f such that ‖f‖ = ∫0∞|f(t)|ω(t)dt < ∞, under pointwise addition, scalar multiplication of functions, and the convolution product (f ⁎ g)(t) = ∫0t f(t - s)g(s)ds. We give a sufficient condition on a weight function ω(t) in order that L1(ω) has a bounded approximate identity.

CONDITIONAL GENERALIZED FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ON A BANACH ALGEBRA

  • Chang, Seung-Jun;Choi, Jae-Gil
    • 대한수학회보
    • /
    • 제41권1호
    • /
    • pp.73-93
    • /
    • 2004
  • In [10], Chang and Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we define the conditional generalized Fourier-Feynman transform and conditional generalized convolution product on function space. We then establish some relationships between the conditional generalized Fourier-Feynman transform and conditional generalized convolution product for functionals on function space that belonging to a Banach algebra.

SHEAF-THEORETIC APPROACH TO THE CONVOLUTION ALGEBRAS ON QUIVER VARIETIES

  • Kwon, Namhee
    • 호남수학학술지
    • /
    • 제35권1호
    • /
    • pp.1-15
    • /
    • 2013
  • In this paper, we study a sheaf-theoretic analysis of the convolution algebra on quiver varieties. As by-products, we reinterpret the results of H. Nakajima. We also produce a refined form of the BBD decomposition theorem for quiver varieties. Finally, we study a construction of highest weight modules through constructible functions.

ANOTHER PROOF THAT Aγ(G) AND A(G) ARE BANACH ALGEBRAS

  • Lee, Hun Hee
    • 충청수학회지
    • /
    • 제24권2호
    • /
    • pp.337-344
    • /
    • 2011
  • We provide another unified proof that $A_{\gamma}(G)$ and $A_{\Delta}(G)$ are Banach algebras for a compact group G, where $A_{\gamma}(G)$ and $A_{\Delta}(G)$ are images of the convolution and the twisted convolution, respectively, on $A(G{\times}G)$. Our new approach heavily depends on analysis of co-multiplication on VN(G), the group von-Neumann algebra of G.

GENERALIZED FIRST VARIATION AND GENERALIZED SEQUENTIAL FOURIER-FEYNMAN TRANSFORM

  • Byoung Soo Kim
    • Korean Journal of Mathematics
    • /
    • 제31권4호
    • /
    • pp.521-536
    • /
    • 2023
  • This paper is a further development of the recent results by the author and coworker on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We establish existence of the generalized first variation of these functionals. Also we investigate various relationships between the generalized sequential Fourier-Feynman transform, the generalized sequential convolution product and the generalized first variation of the functionals.

WEAK AMENABILITY OF CONVOLUTION BANACH ALGEBRAS ON COMPACT HYPERGROUPS

  • Samea, Hojjatollah
    • 대한수학회보
    • /
    • 제47권2호
    • /
    • pp.307-317
    • /
    • 2010
  • In this paper we find necessary and sufficient conditions for weak amenability of the convolution Banach algebras A(K) and $L^2(K)$ for a compact hypergroup K, together with their applications to convolution Banach algebras $L^p(K)$ ($2\;{\leq}\;p\;<\;{\infty}$). It will further be shown that the convolution Banach algebra A(G) for a compact group G is weakly amenable if and only if G has a closed abelian subgroup of finite index.

FOURIER-YEH-FEYNMAN TRANSFORM AND CONVOLUTION ON YEH-WIENER SPACE

  • Kim, Byoung Soo;Yang, Young Kyun
    • Korean Journal of Mathematics
    • /
    • 제16권3호
    • /
    • pp.335-348
    • /
    • 2008
  • We define Fourier-Yeh-Feynman transform and convolution product on the Yeh-Wiener space, and establish the existence of Fourier-Yeh-Feynman transform and convolution product for functionals in a Banach algebra $\mathcal{S}(Q)$. Also we obtain Parseval's relation for those functionals.

  • PDF

MULTIPLE Lp ANALYTIC GENERALIZED FOURIER-FEYNMAN TRANSFORM ON THE BANACH ALGEBRA

  • Chang, Seung-Jun;Choi, Jae-Gil
    • 대한수학회논문집
    • /
    • 제19권1호
    • /
    • pp.93-111
    • /
    • 2004
  • In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $C_{a,\;b}[0,\;T]$. We then verify the existence of the multiple $L_{p}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $S({L_{a,\;b}}^{2}[0, T])$. Finally we establish some relationships between the multiple $L_{p}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $S({L_{a,\;b}}^{2}[0, T])$.

GENERALIZED SEQUENTIAL CONVOLUTION PRODUCT FOR THE GENERALIZED SEQUENTIAL FOURIER-FEYNMAN TRANSFORM

  • Kim, Byoung Soo;Yoo, Il
    • Korean Journal of Mathematics
    • /
    • 제29권2호
    • /
    • pp.321-332
    • /
    • 2021
  • This paper is a further development of the recent results by the authors on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We investigate various relationships between the generalized sequential Fourier-Feynman transform and the generalized sequential convolution product of functionals. Parseval's relation for the generalized sequential Fourier-Feynman transform is also given.