Method of mean value operators for radon transforms in the space of matrices

E. Ournycheva; B. Rubin

doi:10.1142/S0129167X08004686

Method of mean value operators for radon transforms in the space of matrices

E. Ournycheva^*
, B. Rubin

^*Corresponding author for this work

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

5 Scopus citations

Abstract

We extend the FunkRadonHelgason inversion method of mean value operators to the Radon transform f → f̂ of continuous and L(p) functions which are integrated over matrix planes in the space of real rectangular matrices. Necessary and sufficient conditions of existence of f̂ for such f and explicit inversion formulas are obtained. New higher-rank phenomena related to this setting are investigated.

Original language	English
Pages (from-to)	245-283
Number of pages	39
Journal	International Journal of Mathematics
Volume	19
Issue number	3
DOIs	https://doi.org/10.1142/S0129167X08004686
State	Published - Mar 2008
Externally published	Yes

Keywords

Inversion formulas
L-spaces
Matrix spaces
Radon transforms

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10.1142/S0129167X08004686

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title = "Method of mean value operators for radon transforms in the space of matrices",

abstract = "We extend the FunkRadonHelgason inversion method of mean value operators to the Radon transform f → {\^f} of continuous and L(p) functions which are integrated over matrix planes in the space of real rectangular matrices. Necessary and sufficient conditions of existence of {\^f} for such f and explicit inversion formulas are obtained. New higher-rank phenomena related to this setting are investigated.",

keywords = "Inversion formulas, L-spaces, Matrix spaces, Radon transforms",

author = "E. Ournycheva and B. Rubin",

year = "2008",

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AU - Ournycheva, E.

AU - Rubin, B.

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N2 - We extend the FunkRadonHelgason inversion method of mean value operators to the Radon transform f → f̂ of continuous and L(p) functions which are integrated over matrix planes in the space of real rectangular matrices. Necessary and sufficient conditions of existence of f̂ for such f and explicit inversion formulas are obtained. New higher-rank phenomena related to this setting are investigated.

AB - We extend the FunkRadonHelgason inversion method of mean value operators to the Radon transform f → f̂ of continuous and L(p) functions which are integrated over matrix planes in the space of real rectangular matrices. Necessary and sufficient conditions of existence of f̂ for such f and explicit inversion formulas are obtained. New higher-rank phenomena related to this setting are investigated.

KW - Inversion formulas

KW - L-spaces

KW - Matrix spaces

KW - Radon transforms

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SP - 245

EP - 283

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 3

ER -

Method of mean value operators for radon transforms in the space of matrices

Abstract

Keywords

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