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Conditions are given on the sequences $m^{(1)},...,m^{(n)}$ and on the operators $X_{1},...,X_{n}$ so that the equality $S_{\\mathbf{m}}(\\mathbf{X}) = S_{m^{(1)}}(X_{1})\\cap ... \\cap{S}_{m^{(n)}}(X_{n})$ is valid. As a corollary we obtain a new proof of a characterization theorem for clas"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1306.0800","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-04T14:14:45Z","cross_cats_sorted":[],"title_canon_sha256":"3afbeffba3f857ceb2889aeec10883d0c45f3ca1b1687f5e24c4e77e3090b937","abstract_canon_sha256":"a7f303ae1553eaf6ba15490f92fb7b75c04df33d9fecda2950cbadfb4eac961f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:44.928088Z","signature_b64":"TP3GHO2Pzf8g3YSyC8V1PhC9BW9oXu1adCQCKXWt6StGBB4qz/gFnGrNYh+ojrx+UTmgyn4addPNt0QoRbrDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"998f86119c61b7fb571bfa5e194655d6705a3fccf5dbf713d6a53e463d4bb67c","last_reissued_at":"2026-05-18T03:21:44.927541Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:44.927541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the characterization of Gelfand-Shilov-Roumieu spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mihai Pascu","submitted_at":"2013-06-04T14:14:45Z","abstract_excerpt":"Generalized $\\mathbf{m}$-Gelfand-Shilov-Roumieu vector spaces $\\mathcal{S}_{\\mathbf{m}}(\\mathbf{X})$ are introduced. Here $\\mathbf{m} = (m^{(1)},...,m^{(n)})$, $\\mathbf{X}=(X_{1},...,X_{n})$ and $m^{(1)},...,m^{(n)}$ are sequences of positive real numbers and $X_{1},...,X_{n}$ are operators in a Hilbert space. Conditions are given on the sequences $m^{(1)},...,m^{(n)}$ and on the operators $X_{1},...,X_{n}$ so that the equality $S_{\\mathbf{m}}(\\mathbf{X}) = S_{m^{(1)}}(X_{1})\\cap ... \\cap{S}_{m^{(n)}}(X_{n})$ is valid. 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