The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Determining a Function from Its Mean Values Over a Family of Spheres
Abstract
Suppose D is a bounded, connected, open set in R n and f is a smooth function on R n with support in $\overD$. We study the recovery of f from the mean values of f over spheres centered on a part or the whole boundary of D. For strictly convex $\overline{D}$, we prove uniqueness when the centers are restricted to an open subset of the boundary. We provide an inversion algorithm (with proof) when the mean values are known for all spheres centered on the boundary of D, with radii in the interval [0, diam(D)/2]. We also give an inversion formula when D is a ball in R n , $n \geq 3$ and odd, and the mean values are known for all spheres centered on the boundary.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Methods of Mathematical Physics
Courant, R., Hilbert, D., & Teichmann, T. (1962) · Physics Today · doi:10.1063/1.3057861 · Cited by 1,419
Cited by
Photoacoustic tomography: In vivo imaging from organelles to organs
Wang, L. V., & Hu, S. (2012) · Science · doi:10.1126/science.1216210 · Cited by 4,331
Prospects of photoacoustic tomography
Wang, L. V. (2008) · Medical Physics · doi:10.1118/1.3013698 · Cited by 561
Metadata
- Authors
- Finch, D., & Patch, S. K.
- Venue
- SIAM Journal on Mathematical Analysis
- Published
- 2004-01
- Volume
- 35
- Issue
- 5
- Pages
- 1213-1240
- ISSN
- 0036-1410 (ISSN-L)
- 1095-7154
- OpenAlex
- W2149542824
- Cited by
- 410
- References
- 1
- FWCI
- 22.04
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Determining a Function from Its Mean Values Over a Family of Spheres. https://app.cochat.ai/papers/10.1137/s0036141002417814
- The paper
- Finch, D., & Patch, S. K. (2004). Determining a Function from Its Mean Values Over a Family of Spheres. SIAM Journal on Mathematical Analysis. https://doi.org/10.1137/s0036141002417814
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
