scholarly journals Mean Value theorems for multiplicative functions bounded in mean α-power, α >1

1980 ◽  
Vol 29 (2) ◽  
pp. 177-205 ◽  
Author(s):  
P. D. T. A. Elliott
Keyword(s):  
Real Line ◽  
Sufficient Conditions ◽  
Mean Value ◽  
Necessary And Sufficient Conditions ◽  
Multiplicative Functions ◽  
The Real ◽  
Mean Value Theorems ◽  
Necessary And Sufficient

AbstractOn analogy with functions if Lebesuge class Lα on the real line the author considers those multiplicative arthmetic functions which are bounded in mean α>1. Necessary and sufficient conditions are obtained in order that they should have a mean-value, zero or non-zero. An application is made to Ramanujan's τ-function.

scholarly journals The ordering on permutations induced by continuous maps of the real line

1987 ◽  
Vol 7 (2) ◽  
pp. 155-160 ◽  
Author(s):  
Chris Bernhardt
Keyword(s):  
Real Line ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Partial Ordering ◽  
The Real ◽  
Continuous Maps ◽  
Necessary And Sufficient ◽  
Natural Way

AbstractContinuous maps from the real line to itself give, in a natural way, a partial ordering of permutations. This ordering restricted to cycles is studied.Necessary and sufficient conditions are given for a cycle to have an immediate predecessor. When a cycle has an immediate predecessor it is unique; it is shown how to construct it. Every cycle has immediate successors; it is shown how to construct them.

scholarly journals Exponential dichotomy for evolution families on the real line

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
Adina Luminiţa Sasu
Keyword(s):  
Real Line ◽  
Exponential Dichotomy ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Evolution Family ◽  
The Real ◽  
Evolution Families ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair(Lp(ℝ,X),Lq(ℝ,X)). We show that the admissibility of the pair(Lp(ℝ,X),Lq(ℝ,X))is equivalent to the uniform exponential dichotomy of an evolution family if and only ifp≥q. As applications we obtain characterizations for uniform exponential dichotomy of semigroups.

Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Hideto Nakashima
Keyword(s):  
Sufficient Conditions ◽  
Rational Functions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Symmetric Cones ◽  
The Real ◽  
Tube Domains ◽  
Homogeneous Cone ◽  
Necessary And Sufficient ◽  
Relative Invariants

AbstractIn this paper, we give necessary and sufficient conditions for a homogeneous cone Ω to be symmetric in two ways. One is by using the multiplier matrix of Ω, and the other is in terms of the basic relative invariants of Ω. In the latter approach, we need to show that the real parts of certain meromorphic rational functions obtained by the basic relative invariants are always positive on the tube domains over Ω. This is a generalization of a result of Ishi and Nomura [Math. Z. 259 (2008), 604–674].

METHOD OF MEAN VALUE OPERATORS FOR RADON TRANSFORMS IN THE SPACE OF MATRICES

2008 ◽  
Vol 19 (03) ◽  
pp. 245-283 ◽  
Author(s):  
E. OURNYCHEVA ◽  
B. RUBIN
Keyword(s):  
Radon Transform ◽  
Sufficient Conditions ◽  
Mean Value ◽  
Necessary And Sufficient Conditions ◽  
Inversion Method ◽  
Radon Transforms ◽  
Inversion Formulas ◽  
Higher Rank ◽  
Necessary And Sufficient

We extend the Funk–Radon–Helgason inversion method of mean value operators to the Radon transform [Formula: see text] of continuous and Lpfunctions which are integrated over matrix planes in the space of real rectangular matrices. Necessary and sufficient conditions of existence of [Formula: see text] for such f and explicit inversion formulas are obtained. New higher-rank phenomena related to this setting are investigated.

A Subnormal Operator and its Dual

1996 ◽  
Vol 48 (2) ◽  
pp. 381-396
Author(s):  
Robert F. Olin ◽  
Liming Yang
Keyword(s):  
Unit Circle ◽  
Essential Spectrum ◽  
Real Axis ◽  
Additional Assumption ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Subnormal Operator ◽  
The Real ◽  
Necessary And Sufficient

AbstractIt is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. The study of the structure of a cyclic, irreducible, self-dual, subnormal operator is reduced to the operator Sμ with bpeμ = D. Necessary and sufficient conditions for a cyclic subnormal operator Sμ with bpeμ = D to be self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable. Finally, an approach to a general cyclic, self-dual, subnormal operator is discussed.

scholarly journals MEAN VALUE TYPE INEQUALITIES FOR QUASINEARLY SUBHARMONIC FUNCTIONS

2013 ◽  
Vol 55 (2) ◽  
pp. 349-368 ◽  
Author(s):  
OLEKSIY DOVGOSHEY ◽  
JUHANI RIIHENTAUS
Keyword(s):  
Sufficient Conditions ◽  
Continuous Functions ◽  
Mean Value ◽  
Necessary And Sufficient Conditions ◽  
Subharmonic Functions ◽  
Mean Value Inequality ◽  
The Mean ◽  
Mean Value Inequalities ◽  
Necessary And Sufficient ◽  
Bounded Sets

AbstractThe mean value inequality is characteristic for upper semi-continuous functions to be subharmonic. Quasinearly subharmonic functions generalise subharmonic functions. We find the necessary and sufficient conditions under which subsets of balls are big enough for the characterisation of non-negative, quasinearly subharmonic functions by mean value inequalities. Similar result is obtained also for generalised mean value inequalities where, instead of balls, we consider arbitrary bounded sets, which have non-void interiors and instead of the volume of ball some functions depending on the radius of this ball.

scholarly journals Uniqueness of spaces pretangent to metric spaces at infinity

2019 ◽  
Vol 16 (1) ◽  
pp. 57-87
Author(s):  
Oleksiy Dovgoshey ◽  
Victoria Bilet
Keyword(s):  
Metric Space ◽  
Real Line ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Logarithmic Spiral ◽  
Necessary And Sufficient Conditions ◽  
Scaling Sequence ◽  
Necessary And Sufficient

We find the necessary and sufficient conditions under which an unbounded metric space \(X\) has, at infinity, a unique pretangent space \(\Omega^{X}_{\infty,\tilde{r}}\) for every scaling sequence \(\tilde{r}\). In particular, it is proved that \(\Omega^{X}_{\infty,\tilde{r}}\) is unique and isometric to the closure of \(X\) for every logarithmic spiral \(X\) and every \(\tilde{r}\). It is also shown that the uniqueness of pretangent spaces to subsets of a real line is closely related to the ''asymptotic asymmetry'' of these subsets.

CONSTRUCTION AND PROPERTIES OF QUASI RICCI FLAT SPACES

1986 ◽  
Vol 01 (04) ◽  
pp. 997-1007 ◽  
Author(s):  
GUY BONNEAU ◽  
FRANÇOIS DELDUC
Keyword(s):  
String Theory ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Real ◽  
Ricci Flat ◽  
Compact Case ◽  
Flat Manifolds ◽  
Necessary And Sufficient ◽  
Lagrangian Densities ◽  
Torsion Free

We look for the necessary and sufficient conditions for a generalized torsion-free nonlinear σ-model to be one-loop finite. The corresponding metrics are not only Ricci flat ones, but also a larger class we call “quasi Ricci flat” spaces. We give expressions for the corresponding Lagrangian densities in the real and Kähler cases. In the latter, the manifold is shown to be proper, complete and nonhomogeneous. Unfortunately, in the compact case, relevant for string theory, these quasi Ricci flat manifolds become Ricci flat ones.

On a Geometrical Theorem in Exterior Algebra

1967 ◽  
Vol 19 ◽  
pp. 1187-1191
Author(s):  
Daniel Pedoe
Keyword(s):  
Euclidean Plane ◽  
Sufficient Conditions ◽  
Exterior Algebra ◽  
Necessary And Sufficient Conditions ◽  
The Real ◽  
Necessary And Sufficient

In this paper we shall give necessary and sufficient conditions for three lines, passing respectively through the vertices of a proper triangle PQR in the real Euclidean plane, to be concurrent. Of course, the theorem of Ceva deals with this problem, but it is useful to have a criterion which involves only vectors localized at a point O of the plane, and the exterior products of these vectors. Applications are made to theorems which are not easily proved by other methods.

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