Justification of a Wavelet-Based Integral Formula for Solutions of the Wave Equation

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Justification of a Wavelet-Based Integral Formula for Solutions of the Wave Equation. / Gorodnitskiy, E. A.; Perel, M. V.

In: Journal of Mathematical Sciences (United States), Vol. 238, No. 5, 07.05.2019, p. 630-640.

Research output: Contribution to journal › Article › peer-review

Author

Gorodnitskiy, E. A. ; Perel, M. V. / Justification of a Wavelet-Based Integral Formula for Solutions of the Wave Equation. In: Journal of Mathematical Sciences (United States). 2019 ; Vol. 238, No. 5. pp. 630-640.

BibTeX

@article{984bf2c2a6374bfdb78c7010f3186e55,

title = "Justification of a Wavelet-Based Integral Formula for Solutions of the Wave Equation",

abstract = " An integral representation of solutions of the wave equation obtained earlier is studied. The integrand contains weighted localized solutions of the wave equation that depend on parameters, which are variables of integration. Dependent on parameters, a family of localized solutions is constructed from one solution by means of transformations of shift, scaling, and the Lorentz transform. Sufficient conditions are derived, which ensure the pointwise convergence of the obtained improper integral in the space of parameters. The convergence of this integral in ℒ 2 norm is proved as well. Bibliography: 22 titles. ",

author = "Gorodnitskiy, {E. A.} and Perel, {M. V.}",

year = "2019",

month = may,

day = "7",

doi = "10.1007/s10958-019-04262-5",

language = "English",

volume = "238",

pages = "630--640",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Justification of a Wavelet-Based Integral Formula for Solutions of the Wave Equation

AU - Gorodnitskiy, E. A.

AU - Perel, M. V.

PY - 2019/5/7

Y1 - 2019/5/7

N2 - An integral representation of solutions of the wave equation obtained earlier is studied. The integrand contains weighted localized solutions of the wave equation that depend on parameters, which are variables of integration. Dependent on parameters, a family of localized solutions is constructed from one solution by means of transformations of shift, scaling, and the Lorentz transform. Sufficient conditions are derived, which ensure the pointwise convergence of the obtained improper integral in the space of parameters. The convergence of this integral in ℒ 2 norm is proved as well. Bibliography: 22 titles.

AB - An integral representation of solutions of the wave equation obtained earlier is studied. The integrand contains weighted localized solutions of the wave equation that depend on parameters, which are variables of integration. Dependent on parameters, a family of localized solutions is constructed from one solution by means of transformations of shift, scaling, and the Lorentz transform. Sufficient conditions are derived, which ensure the pointwise convergence of the obtained improper integral in the space of parameters. The convergence of this integral in ℒ 2 norm is proved as well. Bibliography: 22 titles.

UR - http://www.scopus.com/inward/record.url?scp=85064892608&partnerID=8YFLogxK

U2 - 10.1007/s10958-019-04262-5

DO - 10.1007/s10958-019-04262-5

M3 - Article

AN - SCOPUS:85064892608

VL - 238

SP - 630

EP - 640

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 42281561