Mahya Ghandehari

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Publications (7)0 Total impact

  • Article: Some Beurling-Fourier algebras on compact groups are operator algebras
    Mahya Ghandehari, Hun Hee Lee, Ebrahim Samei, Nico Spronk
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    ABSTRACT: Let $G$ be a compact connected Lie group. The question of when a weighted Fourier algebra on $G$ is completely isomorphic to an operator algebra will be investigated in this paper. We will demonstrate that the dimension of the group plays an important role in the question. More precisely, we will get a positive answer to the question when we consider a polynomial type weight coming from a length function on $G$ with the order of growth strictly bigger than the half of the dimension of the group. The case of SU(n) will be examined, focusing more on the details including negative results. The proof for the positive directions depends on a non-commutative version of Littlewood multiplier theory, which we will develop in this paper, and the negative directions will be taken care of by restricting to a maximal torus.
    08/2012;
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    Article: Amenability properties of Rajchman algebras
    Mahya Ghandehari
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    ABSTRACT: Rajchman measures of locally compact Abelian groups are studied for almost a century now, and they play an important role in the study of trigonometric series. Eymard's influential work allowed generalizing these measures to the case of \emph{non-Abelian} locally compact groups $G$. The Rajchman algebra of $G$, which we denote by $B_0(G)$, is the set of all elements of the Fourier-Stieltjes algebra that vanish at infinity. In the present article, we characterize the locally compact groups that have amenable Rajchman algebras. We show that $B_0(G)$ is amenable if and only if $G$ is compact and almost Abelian. On the other extreme, we present many examples of locally compact groups, such as non-compact Abelian groups and infinite solvable groups, for which $B_0(G)$ fails to even have an approximate identity.
    02/2011;
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    Article: Amenability constants for semilattice algebras
    Mahya Ghandehari, Hamed Hatami, Nico Spronk
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    ABSTRACT: For any finite unital commutative idempotent semigroup S, a unital semilattice, we show how to compute the amenability constant of its semigroup algebra l^1(S), which is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. We show that there is no commutative semilattice with amenability constant between 5 and 9.
    05/2007;
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    Article: On the size of the minimum critical set of a Latin square
    Mahya Ghandehari, Hamed Hatami, Ebadollah S. Mahmoodian
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    ABSTRACT: A critical set in an $n \times n$ array is a set $C$ of given entries, such that there exists a unique extension of $C$ to an $n\times n$ Latin square and no proper subset of $C$ has this property. For a Latin square $L$, $\scs{L}$ denotes the size of the smallest critical set of $L$, and $\scs{n}$ is the minimum of $\scs{L}$ over all Latin squares $L$ of order $n$. We find an upper bound for the number of partial Latin squares of size $k$ and prove that $$n^2-(e+o(1))n^{10/6} \le \max \scs{L} \le n^2-\frac{\sqrt{\pi}}{2}n^{9/6}.$$ % This improves a result of N. Cavenagh (Ph.D. thesis, The University of Queensland, 2003) and disproves one of his conjectures. Also it improves the previously known lower bound for the size of the largest critical set of any Latin square of order $n$.
    01/2007;
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    Article: Fourier analysis and large independent sets in powers of complete graphs
    Mahya Ghandehari, Hamed Hatami
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    ABSTRACT: For constant $r$ and arbitrary $n$, it was known that in the graph $K_r^n$ any independent set of size close to the maximum is close to some independent set of maximum size. We prove that this statement holds for arbitrary $r$ and $n$.
    01/2007;
  • Article: A Note on Independent Dominating Sets
    Mahya Ghandehari
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    ABSTRACT: It has been shown by Carsten Thomassen that when r is suciently large, Lovasz Local Lemma can be applied to show that every Hamiltonian r-regular graph has a second Hamiltonian cycle. The best result obtained by this method is the existence of second Hamiltonian cycles in Hamiltonian r-regular graphs, when r 73. In this note we show that by using Lopsided Local Lemma this can be improved to r 48. We also show that Thomassen's condition for the existence of red-independent green-dominating sets is near optimal.
    04/2004;
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    Article: Circular Chromatic Index of Graphs of Maximum Degree 3
    Peyman Afshani, Mahsa Ghandehari, Mahya Ghandehari, Hamed Hatami, Ruzbeh Tusserkani, Xuding Zhu
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    ABSTRACT: This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then c (G) 11=3 provided that G does not contain H1 or H2 as a subgraph, where H1 and H2 are obtained by subdividing one edge of K 2 (the graph with three parallel edges between two vertices) and K4 , respectively. As c (H1) = c (H2) = 4, our result implies that there is no graph G with 11=3 < c (G) < 4. It also implies that if G is a 2-edge connected cubic graph, then (G) 11=3. 1
    03/2004;
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