Access the full text.
Sign up today, get DeepDyve free for 14 days.
In this article, an inversion formula is obtained for the spherical transform which integrates functions, defined on the unit sphere $$S^{2}$$ S 2 , on circles. The inversion formula is for the case where the circles of integration are obtained by intersections of $$S^{2}$$ S 2 with hyperplanes passing through a common point $$\overline{a}$$ a ¯ strictly inside $$S^{2}$$ S 2 . In particular, this yields inversion formulas for two well-known special cases. The first inversion formula is for the special case where the family of circles of integration consists of great circles; this formula is obtained by taking $$\overline{a} = 0$$ a ¯ = 0 . The second inversion formula is for the special case where the circles of integration pass through a common point $$p$$ p on $$S^{2}$$ S 2 ; this formula is obtained by taking the limit $$\overline{a}\rightarrow p$$ a ¯ → p .
Analysis and Mathematical Physics – Springer Journals
Published: May 9, 2015
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.