Nonuniqueness in theS-matrix reduction by means of the asymptotic condition — I

1964 ◽  
Vol 32 (5) ◽  
pp. 1202-1216
Author(s):  
F. Kaschluhn ◽  
E. Wieczorek
Keyword(s):  
Asymptotic Condition ◽  
Matrix Reduction ◽  
Thes Matrix

On a singular eigenvalue problem

1968 ◽  
Vol 64 (2) ◽  
pp. 439-446 ◽  
Author(s):  
D. Naylor ◽  
S. C. R. Dennis
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Bessel Functions ◽  
Asymptotic Condition ◽  
Real Constant ◽  
Limit Circle ◽  
Expansion In Eigenfunctions ◽  
Image Position

Sears and Titchmarsh (1) have formulated an expansion in eigenfunctions which requires a knowledge of the s-zeros of the equationHere ka > 0 is supposed given and β is a real constant such that 0 ≤ β < π. The above equation is encountered when one seeks the eigenfunctions of the differential equationon the interval 0 < α ≤ r < ∞ subject to the condition of vanishing at r = α. Solutions of (2) are the Bessel functions J±is(kr) and every solution w of (2) is such that r−½w(r) belongs to L2 (α, ∞). Since the problem is of the limit circle type at infinity it is necessary to prescribe a suitable asymptotic condition there to make the eigenfunctions determinate. In the present instance this condition is

Eigenphases of theS-matrix at high energy

1973 ◽  
Vol 14 (1) ◽  
pp. 21-51 ◽  
Author(s):  
L. Sertorio ◽  
M. Toller
Keyword(s):  
High Energy ◽  
Thes Matrix

Variational Methods on Finite Dimensional Banach Spaces and Discrete Problems

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Gabriele Bonanno ◽  
Pasquale Candito ◽  
Giuseppina D’Aguí
Keyword(s):  
Variational Methods ◽  
Nonlinear Term ◽  
Asymptotic Condition ◽  
Multiplicity Results ◽  
Order Difference ◽  
Existence And Multiplicity ◽  
Finite Dimensional ◽  
Superlinear Growth ◽  
Discrete Problems ◽  
Minimum Theorem

AbstractIn this paper, existence and multiplicity results for a class of second-order difference equations are established. In particular, the existence of at least one positive solution without requiring any asymptotic condition at infinity on the nonlinear term is presented and the existence of two positive solutions under a superlinear growth at infinity of the nonlinear term is pointed out. The approach is based on variational methods and, in particular, on a local minimum theorem and its variants. It is worth noticing that, in this paper, some classical results of variational methods are opportunely rewritten by exploiting fully the finite dimensional framework in order to obtain novel results for discrete problems.

scholarly journals A Theorem of Galambos-Bojanić-Seneta Type

2009 ◽  
Vol 2009 ◽  
pp. 1-6 ◽  
Author(s):  
Dragan Djurčić ◽  
Aleksandar Torgašev
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Condition ◽  
The Given

In the theorems of Galambos-Bojanić-Seneta's type, the asymptotic behavior of the functions , for , is investigated by the asymptotic behavior of the given sequence of positive numbers , as and vice versa. The main result of this paper is one theorem of such a type for sequences of positive numbers which satisfy an asymptotic condition of the Karamata type  , for .

Elementary matrix reduction over Bézout domains

2019 ◽  
Vol 18 (08) ◽  
pp. 1950141
Author(s):  
Huanyin Chen ◽  
Marjan Sheibani Abdolyousefi
Keyword(s):  
Elementary Divisor ◽  
Bezout Domain ◽  
Elementary Matrix ◽  
Matrix Reduction ◽  
Elementary Divisor Ring ◽  
Bezout Domains ◽  
Diagonal Reduction

A ring [Formula: see text] is an elementary divisor ring if every matrix over [Formula: see text] admits a diagonal reduction. If [Formula: see text] is an elementary divisor domain, we prove that [Formula: see text] is a Bézout duo-domain if and only if for any [Formula: see text], [Formula: see text] such that [Formula: see text]. We explore certain stable-like conditions on a Bézout domain under which it is an elementary divisor ring. Many known results are thereby generalized to much wider class of rings.

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