dc.contributor.author
Ballús Santacana, Andreu
dc.date.accessioned
2026-01-20T19:59:49Z
dc.date.available
2026-01-20T19:59:49Z
dc.identifier
https://ddd.uab.cat/record/324650
dc.identifier
urn:10.48550/arXiv.2506.06885
dc.identifier
urn:oai:ddd.uab.cat:324650
dc.identifier
urn:oai:egreta.uab.cat:publications/73a32e21-2c5c-4cb9-af8c-cc878532926a
dc.identifier
urn:pure_id:517311292
dc.identifier.uri
http://hdl.handle.net/2072/489149
dc.description.abstract
We show that the classical volume formula for the unit x-ball, Vx= πx/2 Γ(x/2+1) , can be characterized as the unique analytic continuation of Haar measure normalization and unit ball volumes for O(n),under principles of categorical invariance and normalization at integer dimensions.We generalize this result to the unitary and symplectic cases, formalize invariance using categorical language, and construct explicit categorical examples with functorial diagrams. This perspective positions Vx and its analogues as canonical analytic objects at the interface of analysis,representation theory,and category theory,and motivates a broader program of exploring categorical invariants for interpolated symmetry.
dc.format
application/pdf
dc.rights
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dc.rights
https://creativecommons.org/licenses/by/4.0/
dc.title
Analytic Uniqueness of Ball Volume Interpolation : Categorical Invariance and Universal Characterization
