2,858 research outputs found
Reduced spectral synthesis and compact operator synthesis
We introduce and study the notion of reduced spectral synthesis, which
unifies the concepts of spectral synthesis and uniqueness in locally compact
groups. We exhibit a number of examples and prove that every non-discrete
locally compact group with an open abelian subgroup has a subset that fails
reduced spectral synthesis. We introduce compact operator synthesis as an
operator algebraic counterpart of this notion and link it with other
exceptional sets in operator algebra theory, studied previously. We show that a
closed subset of a second countable locally compact group satisfies
reduced local spectral synthesis if and only if the subset of satisfies compact operator synthesis. We apply
our results to questions about the equivalence of linear operator equations
with normal commuting coefficients on Schatten -classes.Comment: 43 page
Closable Multipliers
Let (X,m) and (Y,n) be standard measure spaces. A function f in
is called a (measurable) Schur multiplier if
the map , defined on the space of Hilbert-Schmidt operators from
to by multiplying their integral kernels by f, is bounded
in the operator norm.
The paper studies measurable functions f for which is closable in the
norm topology or in the weak* topology. We obtain a characterisation of
w*-closable multipliers and relate the question about norm closability to the
theory of operator synthesis. We also study multipliers of two special types:
if f is of Toeplitz type, that is, if f(x,y)=h(x-y), x,y in G, where G is a
locally compact abelian group, then the closability of f is related to the
local inclusion of h in the Fourier algebra A(G) of G. If f is a divided
difference, that is, a function of the form (h(x)-h(y))/(x-y), then its
closability is related to the "operator smoothness" of the function h. A number
of examples of non-closable, norm closable and w*-closable multipliers are
presented.Comment: 35 page
CLINICAL AND EXPERIMENTAL-PSYCHOLOGICAL STUDY OF PATIENTS WITH PARANOID SCHIZOPHRENIA WITH THE SYNDROME OF PSYCHIC AUTOMATISM
No abstrac
Reduced synthesis in harmonic analysis and compact synthesis in operator theory
The notion of reduced synthesis in the context of harmonic analysis on general locally compact groups is introduced; in the classical situation of commutative groups, this notion means that a function f in the Fourier algebra is annihilated by any pseudofunction supported on f −1(0). A relationship between reduced synthesis and compact synthesis (i.e., the possibility of approximating compact operators by pseudointegral ones without increasing the support) is determined, which makes it possible to obtain new results both in operator theory and in harmonic analysis. Applications to the theory of linear operator equations are also given
Four Dimensional CFT Models with Rational Correlation Functions
Recently established rationality of correlation functions in a globally
conformal invariant quantum field theory satisfying Wightman axioms is used to
construct a family of soluble models in 4-dimensional Minkowski space-time. We
consider in detail a model of a neutral scalar field of dimension 2. It
depends on a positive real parameter c, an analogue of the Virasoro central
charge, and admits for all (finite) c an infinite number of conserved symmetric
tensor currents. The operator product algebra of is shown to coincide
with a simpler one, generated by a bilocal scalar field of
dimension (1,1). The modes of V together with the unit operator span an
infinite dimensional Lie algebra whose vacuum (i.e. zero energy lowest
weight) representations only depend on the central charge c. Wightman
positivity (i.e. unitarity of the representations of ) is proven to be
equivalent to .Comment: 28 pages, LATEX, amsfonts, latexsym. Proposition 2.3, and Conjecture
in Sec. 6 are revised. Minor errors are correcte
The value of endo rectal ultrasound
In the last twenty years, endorectal ultrasound (ERUS) has become the primary method for locoregional staging of rectal cancer. ERUS is the most accurate modality for assessing local depth of invasion of rectal carcinoma into the rectal wall layers (T stage). Lower accuracy for T2 tumors is commonly reported, which could lead to sonographic overstaging of T3 tumors following preoperative therapy. Unfortunately, ERUS is not as good for predicting nodal metastases as it is for tumor depth, which could be related to the unclear definition of nodal metastases. The use of multiple criteria might improve accuracy. Failure to evaluate nodal statuscould lead to inadequate surgical resection. ERUS can accurately distinguish early cancers from advanced ones, with a high detection rate of residual carcinoma in the rectal wall. ERUS is also useful for detection of local recurrence at the anastomosis site, which might require fine-needle aspiration of the tissue. Overstaging is more frequent than understaging, mostly due to inflammatory changes. Limitations of ERUS are operator and experience dependency, limited tolerance of patients, and limited range of depth of the transducer. The ERUS technique requires a learning curve for orientation and identification of images and planes. With sufficient time and effort, quality and accuracy of the ERUS procedure could be improved
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