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This paper establishes a close connection between the asymptotic Nikolskii constant, $$ \\mathcal{L}^\\ast(d):=\\lim_{n\\to \\infty} \\frac 1 {\\dim \\Pi_n^d} \\sup_{f\\in \\Pi_n^d} \\frac { \\|f\\|_{L^\\infty(\\mathbb{S}^d)}}{\\|f\\|_{L^1(\\mathbb{S}^d)}},$$ and the following extremal problem: $$ \\mathcal{I}_\\alpha:=\\inf_{a_k} \\Bigl\\| j_{\\alpha+1} (t)- \\sum_{k=1}^\\i"},"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":"1907.03832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-08T19:55:17Z","cross_cats_sorted":[],"title_canon_sha256":"6bdcb440be5696787ebe6fb529ef5b86c69fcb7e91ccea0a71e7a45bd6f715c4","abstract_canon_sha256":"97d315c21ba4ee2b6b913cee564e6960dbf09973488384354a0045441459a6e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:06.701877Z","signature_b64":"Q1+TKcUGyfAHr+Q+WUI3aj56EvWdIQbiWtobr3MfiV5piotUQHZD9KFThTHv6Q/I7Ne+6tnD9rdxwIcIZlbNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e5eab34ff50045c8ae6b0763382bdde5f973a17a79dab65f3ec9bd65a85d243","last_reissued_at":"2026-05-17T23:41:06.701068Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:06.701068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimates of the asymptotic Nikolskii constants for spherical polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dmitry Gorbachev, Feng Dai, Sergey Tikhonov","submitted_at":"2019-07-08T19:55:17Z","abstract_excerpt":"Let $\\Pi_n^d$ denote the space of spherical polynomials of degree at most $n$ on the unit sphere $\\mathbb{S}^d\\subset \\mathbb{R}^{d+1}$ that is equipped with the surface Lebesgue measure $d\\sigma$ normalized by $\\int_{\\mathbb{S}^d} \\, d\\sigma(x)=1$. This paper establishes a close connection between the asymptotic Nikolskii constant, $$ \\mathcal{L}^\\ast(d):=\\lim_{n\\to \\infty} \\frac 1 {\\dim \\Pi_n^d} \\sup_{f\\in \\Pi_n^d} \\frac { \\|f\\|_{L^\\infty(\\mathbb{S}^d)}}{\\|f\\|_{L^1(\\mathbb{S}^d)}},$$ and the following extremal problem: $$ \\mathcal{I}_\\alpha:=\\inf_{a_k} \\Bigl\\| j_{\\alpha+1} (t)- \\sum_{k=1}^\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03832","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.03832","created_at":"2026-05-17T23:41:06.701210+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.03832v1","created_at":"2026-05-17T23:41:06.701210+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03832","created_at":"2026-05-17T23:41:06.701210+00:00"},{"alias_kind":"pith_short_12","alias_value":"LZPKWNH7KACF","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"LZPKWNH7KACFZCXG","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"LZPKWNH7","created_at":"2026-05-18T12:33:21.387695+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LZPKWNH7KACFZCXGWB3DHAV53Z","json":"https://pith.science/pith/LZPKWNH7KACFZCXGWB3DHAV53Z.json","graph_json":"https://pith.science/api/pith-number/LZPKWNH7KACFZCXGWB3DHAV53Z/graph.json","events_json":"https://pith.science/api/pith-number/LZPKWNH7KACFZCXGWB3DHAV53Z/events.json","paper":"https://pith.science/paper/LZPKWNH7"},"agent_actions":{"view_html":"https://pith.science/pith/LZPKWNH7KACFZCXGWB3DHAV53Z","download_json":"https://pith.science/pith/LZPKWNH7KACFZCXGWB3DHAV53Z.json","view_paper":"https://pith.science/paper/LZPKWNH7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.03832&json=true","fetch_graph":"https://pith.science/api/pith-number/LZPKWNH7KACFZCXGWB3DHAV53Z/graph.json","fetch_events":"https://pith.science/api/pith-number/LZPKWNH7KACFZCXGWB3DHAV53Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LZPKWNH7KACFZCXGWB3DHAV53Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LZPKWNH7KACFZCXGWB3DHAV53Z/action/storage_attestation","attest_author":"https://pith.science/pith/LZPKWNH7KACFZCXGWB3DHAV53Z/action/author_attestation","sign_citation":"https://pith.science/pith/LZPKWNH7KACFZCXGWB3DHAV53Z/action/citation_signature","submit_replication":"https://pith.science/pith/LZPKWNH7KACFZCXGWB3DHAV53Z/action/replication_record"}},"created_at":"2026-05-17T23:41:06.701210+00:00","updated_at":"2026-05-17T23:41:06.701210+00:00"}