Unitarity and asymptotic condition in a model with dipole ghost

2005 ◽  
pp. 196-198
Author(s):  
K. Sekine
Keyword(s):  
Asymptotic Condition

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

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.

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

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 .

The interaction between inner and outer regions of turbulent wall-bounded flow

2007 ◽  
Vol 365 (1852) ◽  
pp. 683-698 ◽  
Author(s):  
Jonathan F Morrison
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Low Frequency ◽  
Linear Process ◽  
Asymptotic Condition ◽  
Outer Scale ◽  
Active Motion ◽  
High Reynolds ◽  
Scale Motion ◽  
Turbulent Wall

The nature of the interaction between the inner and outer regions of turbulent wall-bounded flow is examined. Townsend's theory of inactive motion is shown to be a first-order, linear approximation of the effect of the large eddies at the surface that acts as a quasi-inviscid, low-frequency modulation of the shear-stress-bearing motion. This is shown to be a ‘strong’ asymptotic condition that directly expresses the decoupling of the inner-scale active motion from the outer-scale inactive motion. It is further shown that such a decoupling of the inner and outer vorticity fields near the wall is inappropriate, even at high Reynolds numbers, and that a ‘weak’ asymptotic condition is required to represent the increasing effect of outer-scale influences as the Reynolds number increases. High Reynolds number data from a fully developed pipe flow and the atmospheric surface layer are used to show that the large-scale motion penetrates to the wall, the inner–outer interaction is not describable as a linear process and the interaction should more generally be accepted as an intrinsically nonlinear one.

Asymptotic condition in the Lorentz gauge

1961 ◽  
Vol 21 (5) ◽  
pp. 867-868
Author(s):  
M. Wellner
Keyword(s):  
Asymptotic Condition ◽  
Lorentz Gauge

Asymptotische Mehrteilchen-Feldoperatoren für phänomenologische Potentiale

1968 ◽  
Vol 23 (11) ◽  
pp. 1834-1840
Author(s):  
Peter Natusch
Keyword(s):  
Hilbert Space ◽  
Angular Momentum ◽  
Scattering Theory ◽  
Time Dependent ◽  
Asymptotic Condition ◽  
Multichannel Scattering ◽  
Theoretical Formulation ◽  
Special Subset ◽  
Dependent Field

In W. Sandhas’ field theoretical formulation1 of the nonrelativistic multichannel scattering theory the existence of asymptotic multiparticle field operators is discussed for phenomenological potentials. For potentials with momentum-dependent terms it is necessary to treat the convergence of time-dependent field operators on a special subset, — dense in the Hilbert space of states; concerning the position-dependency of tensor- and angular momentum-forces it is necessary to make use of a sharpened asymptotic condition.

Sign in / Sign up

Export Citation Format

Share Document