scholarly journals Characterization of a resistive half plane over a resistive sheet

1993 ◽  
Vol 41 (8) ◽  
pp. 1063-1068 ◽  
Author(s):  
J.R. Natzke ◽  
J.L. Volakis
Keyword(s):  
Half Plane ◽  
Resistive Sheet

On Uniqueness of Dirichlet Series

2020 ◽  
Author(s):  
Bao Qin Li
Keyword(s):  
Analytic Continuation ◽  
Dirichlet Series ◽  
Finite Order ◽  
Half Plane ◽  
Complex Plane ◽  
Meromorphic Functions ◽  
Uniqueness Problem ◽  
Uniqueness Theorems

Abstract We give a characterization of the ratio of two Dirichelt series convergent in a right half-plane under an analytic condition, which is applicable to a uniqueness problem for Dirichlet series admitting analytic continuation in the complex plane as meromorphic functions of finite order; uniqueness theorems are given in terms of a-points of the functions.

scholarly journals On Combinatorial Depth Measures

2018 ◽  
Vol 28 (04) ◽  
pp. 381-398
Author(s):  
Stephane Durocher ◽  
Robert Fraser ◽  
Alexandre Leblanc ◽  
Jason Morrison ◽  
Matthew Skala
Keyword(s):  
Convex Hull ◽  
Half Plane ◽  
Combinatorial Complexity ◽  
Query Point ◽  
Combinatorial Characterization ◽  
Simplicial Depth ◽  
Natural Measures

Given a set [Formula: see text] of points and a point [Formula: see text] in the plane, we define a function [Formula: see text] that provides a combinatorial characterization of the multiset of values [Formula: see text], where for each [Formula: see text], [Formula: see text] is the open half-plane determined by [Formula: see text] and [Formula: see text]. We introduce two new natural measures of depth, perihedral depth and eutomic depth, and we show how to express these and the well-known simplicial and Tukey depths concisely in terms of [Formula: see text]. The perihedral and eutomic depths of [Formula: see text] with respect to [Formula: see text] correspond respectively to the number of subsets of [Formula: see text] whose convex hull contains [Formula: see text], and the number of combinatorially distinct bisections of [Formula: see text] determined by a line through [Formula: see text]. We present algorithms to compute the depth of an arbitrary query point in [Formula: see text] time and medians (deepest points) with respect to these depth measures in [Formula: see text] and [Formula: see text] time respectively. For comparison, these results match or slightly improve on the corresponding best-known running times for simplicial depth, whose definition involves similar combinatorial complexity.

scholarly journals STEINER POLYNOMIALS VIA ULTRA-LOGCONCAVE SEQUENCES

2012 ◽  
Vol 14 (06) ◽  
pp. 1250040 ◽  
Author(s):  
MARTIN HENK ◽  
MARÍA A. HERNÁNDEZ CIFRE ◽  
EUGENIA SAORÍN
Keyword(s):  
Structural Properties ◽  
Real Axis ◽  
Half Plane ◽  
Convex Bodies ◽  
Positive Real Axis ◽  
Complex Root ◽  
Positive Real ◽  
Stable Polynomials ◽  
Upper Half Plane

We investigate structural properties of the cone of roots of relative Steiner polynomials of convex bodies. We prove that they are closed, monotonous with respect to the dimension, and that they cover the whole upper half-plane, except the positive real axis, when the dimension tends to infinity. In particular, it turns out that relative Steiner polynomials are stable polynomials if and only if the dimension is ≤ 9. Moreover, pairs of convex bodies whose relative Steiner polynomial has a complex root on the boundary of such a cone have to satisfy some Aleksandrov–Fenchel inequality with equality. An essential tool for the proofs of the results is the characterization of Steiner polynomials via ultra-logconcave sequences.

scholarly journals Schatten Class Operators in ℒ(La2(ℂ+)) \msbm=MTMIB${\cal L}\left( {L_a^2 \left( {{\msbm C}_+ } \right)} \right)$

2017 ◽  
Vol 55 (2) ◽  
pp. 91-117
Author(s):  
Namita Das ◽  
Jitendra Kumar Behera
Keyword(s):  
Bergman Space ◽  
Half Plane ◽  
Toeplitz Operators ◽  
Hankel Operators ◽  
Bounded Operators ◽  
Area Measure ◽  
Schatten Class ◽  
The Right

AbstractIn this paper, we consider Toeplitz operators defined on the Bergman space\msbm=MTMIB$L_a^2 \left( {{\msbm C}_+ } \right)$of the right half plane and obtain Schatten class characterization of these operators. We have shown that if the Toeplitz operators 𝕿φon\msbm=MTMIB$L_a^2 \left( {{\msbm C}_+ } \right)$belongs to the Schatten classSp, 1 ≤p < ∞,then\msbm=MTMIB$\tilde \phi \in L^p \left( {{\msbm C}_+ ,d\nu } \right)$, where$\tilde \phi \left( w \right) = \left\langle {\phi b_{\bar w} ,b_{\bar w} } \right\rangle $w ∈ℂ+and$b_{\bar w} (s) = {1 \over {\sqrt \pi }}{{1 + w} \over {1 + \bar w}}{{2 Rew} \over {\left( {s + w} \right)^2 }}$. Here$d\nu (w) = \left| {B(\bar w,w)} \right|d\mu (w)$, wheredμ(w) is the area measure on ℂ+and$B(\bar w,w) = \left( {b_{\bar w} (\bar w)} \right)^2 $: Furthermore, we show that ifφ ∈ Lp(ℂ+,dv),then\msbm=MTMIB$\tilde \phi \in L^p ({\msbm C}_+ ,d\nu )$and 𝕿φ∈Sp. We also use these results to obtain Schatten class characterizations of little Hankel operators and bounded operators defined on the Bergman space\msbm=MTMIB$L_a^2 \left( {{\msbm C}_+ } \right)$

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