60,140 research outputs found
Distances between composition operators
The norm distance between two composition operators is calculated in select
cases
A Proof of the Riemann hypothesis The new version contains a change in Definition 3.4, resulting in simpler proofs of theorems in Sections 3 and 4. Also, important proof in Sec.5 has been modified, for completeness and clarity
The function is
analytic and has the same zeros as the Riemann zeta function in the critical
strip . This paper combines some
novel methods about indefinite integration, indefinite convolutions and
inversions of Fourier transforms with numerical ranges of operators to prove
the Riemann hypothesis.Comment: 26 pages in .pdf This version changes Definition 3.4, enabling
changes the statements of Theorems in Sec.4, and thus enabling a clearer
proof in Sec.
Characteristic functions and joint invariant subspaces
Let T:=[T_1,..., T_n] be an n-tuple of operators on a Hilbert space such that
T is a completely non-coisometric row contraction. We establish the existence
of a "one-to-one" correspondence between the joint invariant subspaces under
T_1,..., T_n, and the regular factorizations of the characteristic function
associated with T. In particular, we prove that there is a non-trivial joint
invariant subspace under the operators T_1,..., T_n, if and only if there is a
non-trivial regular factorization of the characteristic function. We also
provide a functional model for the joint invariant subspaces in terms of the
regular factorizations of the characteristic function, and prove the existence
of joint invariant subspaces for certain classes of n-tuples of operators.
We obtain criterions for joint similarity of n-tuples of operators to Cuntz
row isometries. In particular, we prove that a completely non-coisometric row
contraction T is jointly similar to a Cuntz row isometry if and only if the
characteristic function of T is an invertible multi-analytic operator.Comment: 35 page
Free holomorphic functions on the unit ball of B(H)^n
We develop a theory of holomorphic functions in several noncommuting (free)
variables and thus provide a framework for the study of arbitrary n-tuples of
operators. The main topics are the following: Free holomorphic functions and
Hausdorff derivations; Cauchy, Liouville, and Schwartz type results for free
holomorphic functions; Algebras of free holomorphic functions; Free analytic
functional calculus and noncommutative Cauchy transforms; Weierstrass and
Montel theorems for free holomorphic functions; Free pluriharmonic functions
and noncommutative Poisson transforms; Hardy spaces of free holomorphic
functions.Comment: 51 page
Bounds on positive interior transmission eigenvalues
The paper contains lower bounds on the counting function of the positive
eigenvalues of the interior transmission problem when the latter is elliptic.
In particular, these bounds justify the existence of an infinite set of
interior transmission eigenvalues and provide asymptotic estimates from above
on the counting function for the large values of the wave number. They also
lead to certain important upper estimates on the first few interior
transmission eigenvalues. We consider the classical transmission problem as
well as the case when the inhomogeneous medium contains an obstacle.Comment: We corrected inaccuracies cost by the wrong sign in the Green formula
(17). In particular, the sign in the definition of \sigma was change
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