Sivaram K. Narayan

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We characterize the essentially normal composition operators induced on the Hardy space H2 by linear fractional maps; they are either compact, normal, or (the nontrivial case) induced by parabolic non-automorphisms. These parabolic maps induce the first known examples of nontrivially essentially normal composition operators. In addition we characterize(More)
The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i 6= j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. This paper introduces a new graph parameter, Z(G), that is the minimum size of a zero forcing set of vertices and uses it to bound the minimum rank(More)
Let G = (V, E) be a multigraph with no loops on the vertex set V = {1, 2, . . . , n}. Define S+(G) as the set of symmetric positive semidefinite matrices A = [aij ] with aij 6= 0, i 6= j, if ij ∈ E(G) is a single edge and aij = 0, i 6= j, if ij / ∈ E(G). Let M+(G) denote the maximum multiplicity of zero as an eigenvalue of A ∈ S+(G) and mr+(G) = |G|−M+(G)(More)
A tight frame in R<sup>n</sup> is a redundant system which has a reconstruction formula similar to that of an orthonormal basis. For a unit-norm frame F = {f<sub>i</sub>}<sup>k</sup><sub>i=1</sub>, a scaling is a vector c = (c(l),..., c(k)) &#x03B5; R<sup>k</sup>&#x2265;0 such that {c(i)f<sub>i</sub>}<sup>k</sup><sub>i=1</sub> is a tight frame in(More)
A magic square M is an n-by-n array of numbers whose rows, columns, and the two diagonals sum to μ called the magic sum. If all the diagonals including broken diagonals sum to μ then the magic square is said to be pandiagonal. A regular magic square satisfies the condition that the entries symmetrically placed with respect to the center sum to 2μ n . If the(More)
Let G = (V, E) be a multigraph with no loops on the vertex set V = {1, 2, . . . , n}. Define S+(G) as the set of symmetric positive semidefinite matrices A = [aij ] with aij 6= 0, i 6= j, if ij ∈ E(G) is a single edge and aij = 0, i 6= j, if ij / ∈ E(G). Let M+(G) denote the maximum multiplicity of zero as an eigenvalue of A ∈ S+(G) and mr+(G) = |G|−M+(G)(More)
We consider (and characterize) mainly classes of (positively) stable complex matrices defined via methods of Geršgorin and Lyapunov. Although the real matrices in most of these classes have already been studied, we sometimes improve upon (and even correct) what has been previously published. Many of the classes turn out quite naturally to be products of(More)