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(In a forthcoming paper [2], a further generalization of the conjecture will be given.) We will prove that a weak congruence holds for any cyclic l - extension (Theorem 3.3),
By subtracting suitable linear combinations of the last n − 2d columns (via ECT’s) from the previous d columns, we may assume that the starred block is 0.. These blocks can be
The above theorem obviously has a natural counterpart, consisting of two series of minimax and maximin identities, for µ k’s. We omit stating and proving those, since it can easily
of matrix valued functions is very rich but mainly, perturbations of matrix functions of a complex argument and matrix functions of Hermitian matrices were considered, cf.
In this section, we prove results concerning local (i.e., restricted to proper subspaces) vs global linear dependence of operators that will be used in the proof of Theorem 1.5, and
We will first show that a Brownian bridge that is conditioned to avoid the origin has the same law as a Bessel bridge; and we will then note that the Bessel bridges have a density
The main lemma in the proof of Theorem 1.1 involves estimating the resistances. A combination of the above identities will then yield lower bounds for the hitting times. We then
In this paper we study the
