{"paper":{"title":"Regularity and convergence analysis in Sobolev and H\\\"older spaces for generalized Whittle-Mat\\'ern fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.ME"],"primary_cat":"math.NA","authors_text":"Kristin Kirchner, Sonja G. Cox","submitted_at":"2019-04-13T17:07:04Z","abstract_excerpt":"We analyze several Galerkin approximations of a Gaussian random field $\\mathcal{Z}\\colon\\mathcal{D}\\times\\Omega\\to\\mathbb{R}$ indexed by a Euclidean domain $\\mathcal{D}\\subset\\mathbb{R}^d$ whose covariance structure is determined by a negative fractional power $L^{-2\\beta}$ of a second-order elliptic differential operator $L:= -\\nabla\\cdot(A\\nabla) + \\kappa^2$. Under minimal assumptions on the domain $\\mathcal{D}$, the coefficients $A\\colon\\mathcal{D}\\to\\mathbb{R}^{d\\times d}$, $\\kappa\\colon\\mathcal{D}\\to\\mathbb{R}$, and the fractional exponent $\\beta>0$, we prove convergence in $L_q(\\Omega; H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06569","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1904.06569/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}