The Smoothness of Convolutions of Singular Orbital Measures on Complex Grassmannians
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Bibliographic record
Abstract
It is well known that if G/K is any irreducible symmetric space and a is a continuous orbital measure supported on the double coset KaK, then the convolution product, k a , is absolutely continuous for some suitably large k dim G/K .The minimal value of k is known in some symmetric spaces and in the special case of compact groups or rank one compact symmetric spaces it has even been shown that k a belongs to the smaller space L 2 for some k .Here we prove that this L 2 property holds for all the compact, complex Grassmannian symmetric spaces, SU (p + q)/S(U (p) U (q)).Moreover, for the orbital measures at a dense set of points a, we prove that 2 a L 2 (or 3 a L 2 if p = q ).
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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