Oscillation Properties of Differential Operators and Convolution Operators, and Some Applications

Khoa, Nguen Tkhi Tkh′eu

doi:10.1070/im1990v034n03abeh000674

Math. USSR Izv.

1990

DOI: 10.1070/im1990v034n03abeh000674

|View full text |Cite

Oscillation Properties of Differential Operators and Convolution Operators, and Some Applications

Nguen Tkhi Tkh′eu Khoa¹

Abstract: New direct observation data on the 2s-2p atomic state coherent mixing upon hydrogen atoms passage through a metal-wall slit are presented. The experimental results are interpreted in terms of atomic state interference, the state mixing amplitude being derived directly from the experimental data obtained.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1994

2017

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

The periodic analog of Rolle's theorem for differential operators and approximation by L-splines

Novikov

1994

Math Notes

View full text Add to dashboard Cite

Rolle's theorem, which expresses the relationship between the number of zeros of a differentiable function and the number :of:z~ros in its derivative, plays an important role in solution of problems in diverse areas of mathematics. It is of interest to';~"~tend Rolle's theorem to the case in which the derivative is replaced by a linear differential operator. To a considerable extent, interest in this problem results from the fact that for classes of smooth function defined by differential operators for which the analog of Rolle's theorem holds, many problems are solved in the theory of approximations. These include problems on diameters, quadrature formulas, problems in the theory of splines, and numerous others (see, for example, [1][2][3][4][5][6][7], and their bibliographies).In the first part of this paper, we prove the periodic analog of Rolle's theorem for linear differential operators satisfying certain additional factorizability constraints. We then use this result in the second part of the paper to find exact values for the upper bounds of the slopes of periodic interpolation L-splines. Let T denote the segment [0,27r], with its endpoints identified: for E = T and E = [a, b](-oo < a < b < + oo),

show abstract

The periodic analog of Rolle's theorem for differential operators and approximation by L-splines

Novikov

1994

Math Notes

View full text Add to dashboard Cite

show abstract

Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions

Vinogradov

2017

Sib Math J

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Oscillation Properties of Differential Operators and Convolution Operators, and Some Applications

Cited by 2 publications

References 11 publications

The periodic analog of Rolle's theorem for differential operators and approximation by L-splines

The periodic analog of Rolle's theorem for differential operators and approximation by L-splines

Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions

Contact Info

Product

Resources

About