Invertibility of Nonautonomous Functional-Differential Operators

Abstract

A critical comparison of experimental data and theoretical calculations of the relative strengths for populating the Ar 11 *Se states following high-energy photoionisation ( y , e) and binary (e, 2e) processes is presented. There is a difference in reported pole strengths (peak areas) of the discrete Ar II states (formed by the ejection of a 3s electron) derived from the two techniques. In addition, the lack of strength in the Ar 11 continuum (i.e. for A?++ e) reported in the ( y, e) experiments is in contrast with theoretical calculations and binary (e, 2e) experiments. The possible problems of background subtraction in the ( y , e) experiment are discussed and it is noted that if the background function is determined in a region of the spectrum where considerable strength in the double ionisation continuum exists, the relative strengths for the satellite lines will be systematically underestimated. It is shown that removal of this defect in the interpretation of the ( 7 , e) experiment should result in smaller discrepancies between the ( y , e) and binary (e, 2e) measurements.

Method of local linear approximation in the theory of bounded solutions of nonlinear difference equations

“…This inequality is analogous to (8), and, by virtue of (14) and (16), it coincides with (15). Therefore, according to Theorem 1, for every h = (h n ) n∈Z ∈ l ∞ (Z, R) Eq.…”

“…These operators were studied in [14][15][16][17][18][19][20]. The definition of c-continuous operator that uses locally convergent sequences was proposed by the author (see, e.g., [21,22]).…”

Conditions for the Existence of Almost Periodic Solutions of Nonlinear Difference Equations with Discrete Argument

“…The Favard results were improved by Mukhamadiev [10,11]. The Mukhamadiev theorems were generalized in [12][13][14]. Important results in this direction also belong to Levitan [1], Amerio [15], and Zhikov [16].…”

Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations

“…These operators were studied in [2][3][4][5][6][7][8][9], etc. The definition of c-continuous operator that uses locally convergent sequences was proposed by the author (see, e.g., [10][11][12]).…”