1,358 research outputs found
Symmetric spaces of higher rank do not admit differentiable compactifications
Any nonpositively curved symmetric space admits a topological
compactification, namely the Hadamard compactification. For rank one spaces,
this topological compactification can be endowed with a differentiable
structure such that the action of the isometry group is differentiable.
Moreover, the restriction of the action on the boundary leads to a flat model
for some geometry (conformal, CR or quaternionic CR depending of the space).
One can ask whether such a differentiable compactification exists for higher
rank spaces, hopefully leading to some knew geometry to explore. In this paper
we answer negatively.Comment: 13 pages, to appear in Mathematische Annale
Weyl group multiple Dirichlet series constructed from quadratic characters
We construct multiple Dirichlet series in several complex variables whose
coefficients involve quadratic residue symbols. The series are shown to have an
analytic continuation and satisfy a certain group of functional equations.
These are the first examples of an infinite collection of unstable Weyl group
multiple Dirichlet series in greater than two variables.Comment: incorporated referee's comment
Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables
This paper is devoted to the specific class of pseudoconformal mappings of
quaternion and octonion variables. Normal families of functions are defined and
investigated. Four criteria of a family being normal are proven. Then groups of
pseudoconformal diffeomorphisms of quaternion and octonion manifolds are
investigated. It is proven, that they are finite dimensional Lie groups for
compact manifolds. Their examples are given. Many charactersitic features are
found in comparison with commutative geometry over or .Comment: 55 pages, 53 reference
Convolution-type derivatives, hitting-times of subordinators and time-changed -semigroups
In this paper we will take under consideration subordinators and their
inverse processes (hitting-times). We will present in general the governing
equations of such processes by means of convolution-type integro-differential
operators similar to the fractional derivatives. Furthermore we will discuss
the concept of time-changed -semigroup in case the time-change is
performed by means of the hitting-time of a subordinator. We will show that
such time-change give rise to bounded linear operators not preserving the
semigroup property and we will present their governing equations by using again
integro-differential operators. Such operators are non-local and therefore we
will investigate the presence of long-range dependence.Comment: Final version, Potential analysis, 201
Lieb-Thirring Bound for Schr\"odinger Operators with Bernstein Functions of the Laplacian
A Lieb-Thirring bound for Schr\"odinger operators with Bernstein functions of
the Laplacian is shown by functional integration techniques. Several specific
cases are discussed in detail.Comment: We revised the first versio
A dimensionally continued Poisson summation formula
We generalize the standard Poisson summation formula for lattices so that it
operates on the level of theta series, allowing us to introduce noninteger
dimension parameters (using the dimensionally continued Fourier transform).
When combined with one of the proofs of the Jacobi imaginary transformation of
theta functions that does not use the Poisson summation formula, our proof of
this generalized Poisson summation formula also provides a new proof of the
standard Poisson summation formula for dimensions greater than 2 (with
appropriate hypotheses on the function being summed). In general, our methods
work to establish the (Voronoi) summation formulae associated with functions
satisfying (modular) transformations of the Jacobi imaginary type by means of a
density argument (as opposed to the usual Mellin transform approach). In
particular, we construct a family of generalized theta series from Jacobi theta
functions from which these summation formulae can be obtained. This family
contains several families of modular forms, but is significantly more general
than any of them. Our result also relaxes several of the hypotheses in the
standard statements of these summation formulae. The density result we prove
for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and
improvement
Propensity-matched analysis of patient-reported outcomes for neoadjuvant chemotherapy prior to radical cystectomy
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. Purpose: To evaluate patient-reported outcomes (PROs) for bladder cancer patients undergoing neoadjuvant chemotherapy (NAC) prior to radical cystectomy (RC) using longitudinal data and propensity-matched scoring analyses. Methods: 155 patients with muscle-invasive bladder cancer scheduled for RC completed the European Organization for Research and Treatment of Cancer questionnaires, EORTC QLQ-C30, EORTC QLQ-BLM30, Fear of Recurrence Scale, Mental Health Inventory and Satisfaction with Life Scale within 4 weeks of surgery. A propensity-matched analysis was performed comparing pre-surgery PROs among 101 patients who completed NAC versus 54 patients who did not receive NAC. We also compared PROs pre- and post-chemotherapy for 16 patients who had data available for both time points. Results: In propensity-matched analysis, NAC-treated patients reported better emotional and sexual function, mental health, urinary function and fewer financial concerns compared to those that did not receive NAC. Longitudinal analysis showed increases in fatigue, nausea and appetite loss following chemotherapy. Conclusion: Propensity-matched analysis did not demonstrate a negative effect of NAC on PRO. Several positive associations of NAC were found in the propensity-matched analysis, possibly due to other confounding differences between the two groups or actual clinical benefit. Longitudinal analysis of a small number of patients found small to modest detrimental effects from NAC similar to toxicities previously reported. Our preliminary findings, along with known survival and toxicity data, should be considered in decision-making for NAC
Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions
This paper is aimed to show the essential role played by the theory of
quasi-analytic functions in the study of the determinacy of the moment problem
on finite and infinite-dimensional spaces. In particular, the quasi-analytic
criterion of self-adjointness of operators and their commutativity are crucial
to establish whether or not a measure is uniquely determined by its moments.
Our main goal is to point out that this is a common feature of the determinacy
question in both the finite and the infinite-dimensional moment problem, by
reviewing some of the most known determinacy results from this perspective. We
also collect some properties of independent interest concerning the
characterization of quasi-analytic classes associated to log-convex sequences.Comment: 28 pages, Stochastic and Infinite Dimensional Analysis, Chapter 9,
Trends in Mathematics, Birkh\"auser Basel, 201
Askey-Wilson Type Functions, With Bound States
The two linearly independent solutions of the three-term recurrence relation
of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22],
are slightly modified so as to make it transparent that these functions satisfy
a beautiful symmetry property. It essentially means that the geometric and the
spectral parameters are interchangeable in these functions. We call the
resulting functions the Askey-Wilson functions. Then, we show that by adding
bound states (with arbitrary weights) at specific points outside of the
continuous spectrum of some instances of the Askey-Wilson difference operator,
we can generate functions that satisfy a doubly infinite three-term recursion
relation and are also eigenfunctions of -difference operators of arbitrary
orders. Our result provides a discrete analogue of the solutions of the purely
differential version of the bispectral problem that were discovered in the
pioneering work [8] of Duistermaat and Gr\"unbaum.Comment: 42 pages, Section 3 moved to the end, minor correction
Dominant Topologies in Euclidean Quantum Gravity
The dominant topologies in the Euclidean path integral for quantum gravity
differ sharply according on the sign of the cosmological constant. For
, saddle points can occur only for topologies with vanishing first
Betti number and finite fundamental group. For , on the other hand,
the path integral is dominated by topologies with extremely complicated
fundamental groups; while the contribution of each individual manifold is
strongly suppressed, the ``density of topologies'' grows fast enough to
overwhelm this suppression. The value is thus a sort of boundary
between phases in the sum over topologies. I discuss some implications for the
cosmological constant problem and the Hartle-Hawking wave function.Comment: 14 pages, LaTeX. Minor additions (computability, relation to
``minimal volume'' in topology); error in eqn (3.5) corrected; references
added. To appear in Class. Quant. Gra
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