77,317 research outputs found
Improper filtrations for C*-algebras: spectra of unilateral tridiagonal operators
We extend the results of our previous paper "C*-algebras and numerical linear
algebra" to cover the case of "unilateral" sections. This situation bears a
close resemblance to the case of Toeplitz operators on Hardy spaces, in spite
of the fact that the operators here are far from Toeplitz operators. In
particular, there is a short exact sequence 0 --> K --> A --> B --> 0 whose
properties are essential to the problem of computing the spectra of self
adjoint operators.Comment: 12 pages, AMS-TeX 2.
Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear systems and operator model theory
The Sz.-Nagy--Foias model theory for contraction operators
combined with the Beurling-Lax theorem establishes a correspondence between any
two of four kinds of objects: shift-invariant subspaces, operator-valued inner
functions, conservative discrete-time input/state/output linear systems, and
Hilbert-space contraction operators. We discuss an analogue of
all these ideas in the context of weighted Hardy spaces over the unit disk and
an associated class of hypercontraction operators
Constant sign and nodal solutions for nonhomogeneous Robin boundary value problems with asymmetric reactions
We study a nonlinear, nonhomogeneous elliptic equation with an asymmetric
reaction term depending on a positive parameter, coupled with Robin boundary
conditions. Under appropriate hypotheses on both the leading differential
operator and the reaction, we prove that, if the parameter is small enough, the
problem admits at least four nontrivial solutions: two of such solutions are
positive, one is negative, and one is sign-changing. Our approach is
variational, based on critical point theory, Morse theory, and truncation
techniques.Comment: 22 page
COMMUTATION PROPERTIES OF THE FORM SUM OF POSITIVE, SYMMETRIC OPERATORS
A new construction for the form sum of positive, selfadjoint operators is given in this
paper. The situation is a bit more general, because our aim is to add positive, symmetric
operators. With the help of the used method, some commutation properties of the form sum
extension are observed
Inner multipliers and Rudin type invariant subspaces
Let be a Hilbert space and be
the -valued Hardy space over the unit disc in
. The well known Beurling-Lax-Halmos theorem states that every
shift invariant subspace of other than
has the form , where is an
operator-valued inner multiplier in for some Hilbert space . In this
paper we identify with -valued Hardy
space and classify all such inner
multiplier for which is a Rudin type invariant subspace of
.Comment: 8 page
On the convergence of double integrals and a generalized version of Fubini's theorem on successive integration
Let the function f: \bar{\R}^2_+ \to \C be such that f\in L^1_{\loc}
(\bar{\R}^2_+). We investigate the convergence behavior of the double integral
\int^A_0 \int^B_0 f(u,v) du dv \quad {\rm as} \quad A,B \to
\infty,\leqno(*) where and tend to infinity independently of one
another; while using two notions of convergence: that in Pringsheim's sense and
that in the regular sense. Our main result is the following Theorem 3: If the
double integral (*) converges in the regular sense, or briefly: converges
regularly, then the finite limits and exist uniformly in , respectively;
and This can be considered as a
generalized version of Fubini's theorem on successive integration when f\in
L^1_{\loc} (\bar{\R}^2_+), but
Intuitionistic computability logic
Computability logic (CL) is a systematic formal theory of computational tasks
and resources, which, in a sense, can be seen as a semantics-based alternative
to (the syntactically introduced) linear logic. With its expressive and
flexible language, where formulas represent computational problems and "truth"
is understood as algorithmic solvability, CL potentially offers a comprehensive
logical basis for constructive applied theories and computing systems
inherently requiring constructive and computationally meaningful underlying
logics.
Among the best known constructivistic logics is Heyting's intuitionistic
calculus INT, whose language can be seen as a special fragment of that of CL.
The constructivistic philosophy of INT, however, has never really found an
intuitively convincing and mathematically strict semantical justification. CL
has good claims to provide such a justification and hence a materialization of
Kolmogorov's known thesis "INT = logic of problems". The present paper contains
a soundness proof for INT with respect to the CL semantics. A comprehensive
online source on CL is available at http://www.cis.upenn.edu/~giorgi/cl.htm
Lower-modular elements of the lattice of semigroup varieties. III
We completely determine all lower-modular elements of the lattice of all
semigroup varieties. As a corollary, we show that a lower-modular element of
this lattice is modular.Comment: 10 pages, 1 figur
Notes on planar semimodular lattices. I. Construction
We construct all planar semimodular lattices in three simple steps from the
direct product of two chains.Comment: 13 pages with 9 diagram
Existence of Pseudo Almost Periodic Solutions to Some Classes of Partial Hyperbolic Evolution Equations
The paper examines the existence of pseudo almost periodic solutions to some
classes of partial hyperbolic evolution equations. Namely, sufficient
conditions for the existence and uniqueness of pseudo almost periodic solutions
to those classes of hyperbolic evolution equations are given. Applications
include the existence of pseudo almost periodic solutions to the transport and
heat equations with delay.Comment: 12 page
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