scholarly journals Characterization of Eigenvalues in Spectral Gap for Singular Differential Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Zhaowen Zheng ◽  
Wenju Zhang
Keyword(s):  
Positive Integer ◽  
Spectral Properties ◽  
Differential Operators ◽  
Spectral Gap ◽  
Deficiency Index ◽  
Minimal Operator ◽  
Adjoint Extension

The spectral properties fornorder differential operators are considered. When given a spectral gap(a,b)of the minimal operatorT0with deficiency indexr, arbitrarympointsβi  (i=1,2,…,m)in(a,b), and a positive integer functionpsuch that∑i=1mp(βi)≤r,T0has a self-adjoint extensionT̃such that eachβi  (i=1,2,…,m)is an eigenvalue ofT̃with multiplicity at leastp(βi).

On singular differential operators with positive coefficients

1992 ◽  
Vol 120 (3-4) ◽  
pp. 361-365 ◽  
Author(s):  
Bernd Schultze
Keyword(s):  
Differential Operators ◽  
Deficiency Index ◽  
Minimal Operator ◽  
Positive Coefficients

SynopsisA class of singular real formally self-adjoint differential expressions M on I = [a, = ∞) (a ∈ ℝ), i.e. expressions of the form My = with pj ≧ 0 (j = 0, …, n – 1), pn > 0 is constructed with the following property: For every integer k with 0 ≦ k < n/2 there exists an expression M in this class such that the deficiency index of T0(M) – the minimal operator associated with M – is n + 2k. This generalises a result in [3] and proves part of the McLeod's conjecture.

scholarly journals Reconstruction of Differential Operators with Frozen Argument

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 24
Author(s):  
Oles Dobosevych ◽  
Rostyslav Hryniv
Keyword(s):  
Perturbation Theory ◽  
Spectral Properties ◽  
General Framework ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Complete Characterization ◽  
Rank One Perturbation ◽  
Clear Explanation ◽  
Rank One

We study spectral properties of a wide class of differential operators with frozen arguments by putting them into a general framework of rank-one perturbation theory. In particular, we give a complete characterization of possible eigenvalues for these operators and solve the inverse spectral problem of reconstructing the perturbation from the resulting spectrum. This approach provides a unified treatment of several recent studies and gives a clear explanation and interpretation of the obtained results.

scholarly journals A new characterization of L2(p2)

2020 ◽  
Vol 18 (1) ◽  
pp. 907-915
Author(s):  
Zhongbi Wang ◽  
Chao Qin ◽  
Heng Lv ◽  
Yanxiong Yan ◽  
Guiyun Chen
Keyword(s):  
Positive Integer ◽  
Irreducible Character ◽  
Character Degrees ◽  
Prime Divisors

Abstract For a positive integer n and a prime p, let {n}_{p} denote the p-part of n. Let G be a group, \text{cd}(G) the set of all irreducible character degrees of G , \rho (G) the set of all prime divisors of integers in \text{cd}(G) , V(G)=\left\{{p}^{{e}_{p}(G)}|p\in \rho (G)\right\} , where {p}^{{e}_{p}(G)}=\hspace{.25em}\max \hspace{.25em}\{\chi {(1)}_{p}|\chi \in \text{Irr}(G)\}. In this article, it is proved that G\cong {L}_{2}({p}^{2}) if and only if |G|=|{L}_{2}({p}^{2})| and V(G)=V({L}_{2}({p}^{2})) .

Characterization of the logistic and loglogistic distributions by extreme value related stability with random sample size

1987 ◽  
Vol 24 (04) ◽  
pp. 838-851 ◽  
Author(s):  
W. J. Voorn
Keyword(s):  
Positive Integer ◽  
Sample Size ◽  
Random Variable ◽  
Logistic Distribution ◽  
Size Distributions ◽  
Random Sample Size ◽  
Maximum Value ◽  
Maximum Stability ◽  
Independent Observations

Maximum stability of a distribution with respect to a positive integer random variable N is defined by the property that the type of distribution is not changed when considering the maximum value of N independent observations. The logistic distribution is proved to be the only symmetric distribution which is maximum stable with respect to each member of a sequence of positive integer random variables assuming value 1 with probability tending to 1. If a distribution is maximum stable with respect to such a sequence and minimum stable with respect to another, then it must be logistic, loglogistic or ‘backward' loglogistic. The only possible sample size distributions in these cases are geometric.

A class of symmetric ordinary differential operators whose deficiency numbers differ by an integer†

1978 ◽  
Vol 82 (1-2) ◽  
pp. 117-134 ◽  
Author(s):  
Richard C. Gilbert
Keyword(s):  
Differential Operator ◽  
Positive Integer ◽  
Asymptotic Expansions ◽  
Differential Operators ◽  
Ordinary Differential Operator ◽  
Ordinary Differential Operators ◽  
Half Axis ◽  
Complex Coefficients

SynopsisFormulas are determined for the deficiency numbers of a formally symmetric ordinary differential operator with complex coefficients which have asymptotic expansions of a prescribed type on a half-axis. An implication of these formulas is that for any given positive integer there exists a formally symmetric ordinary differential operator whose deficiency numbers differ by that positive integer.

scholarly journals Characterization of Physical, Thermal and Spectral Properties of Biofield Treated O-Aminophenol

2015 ◽  
Vol 6 (10) ◽  
Author(s):  
Mahendra Kumar Trivedi ◽  
Rama Mohan Tallapragada ◽  
Alice Branton
Keyword(s):  
Spectral Properties ◽  
Thermal And Spectral Properties
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