{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BO3Y4UEV36P5LGRRNFFJSGZIWW","short_pith_number":"pith:BO3Y4UEV","schema_version":"1.0","canonical_sha256":"0bb78e5095df9fd59a31694a991b28b5a485f3a5b2bf83592e13e034c61c6c61","source":{"kind":"arxiv","id":"1702.00875","version":1},"attestation_state":"computed","paper":{"title":"Characterization of Polynomials as solutions of certain functional equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"J. M. Almira","submitted_at":"2017-02-03T00:06:00Z","abstract_excerpt":"Recently, the functional equation \\[ \\sum_{i=0}^mf_i(b_ix+c_iy)= \\sum_{i=1}^na_i(y)v_i(x) \\] with $x,y\\in\\mathbb{R}^d$ and $b_i,c_i\\in\\mathbf{GL}_d(\\mathbb{C})$, was studied by Almira and Shulman, both in the classical context of continuous complex valued functions and in the framework of complex valued Schwartz distributions, where these equations were properly introduced in two different ways. The solution sets of these equations are, typically, exponential polynomials and, in some particular cases, they reduce to ordinary polynomials. In this paper we present several characterizations of or"},"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":"1702.00875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-03T00:06:00Z","cross_cats_sorted":[],"title_canon_sha256":"6b1816e83f7f82e02384ba83189ab8e4f9d8cfe5e043bd3c4e7bf1e8df8f35b6","abstract_canon_sha256":"b2f94b32dc1ca4c01a8775c1a983b67d5cf37a5f678fd6521b9647436eed3a34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:29.538512Z","signature_b64":"aPFstLiPyq9r8kVXoJOzmUqx1i1E+mDx8lSRA7w1ETPmY2NLqrUEdVgjL25Wi9JsrsULCXtZ/BBmr0XTny8BAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bb78e5095df9fd59a31694a991b28b5a485f3a5b2bf83592e13e034c61c6c61","last_reissued_at":"2026-05-18T00:51:29.538061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:29.538061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterization of Polynomials as solutions of certain functional equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"J. M. Almira","submitted_at":"2017-02-03T00:06:00Z","abstract_excerpt":"Recently, the functional equation \\[ \\sum_{i=0}^mf_i(b_ix+c_iy)= \\sum_{i=1}^na_i(y)v_i(x) \\] with $x,y\\in\\mathbb{R}^d$ and $b_i,c_i\\in\\mathbf{GL}_d(\\mathbb{C})$, was studied by Almira and Shulman, both in the classical context of continuous complex valued functions and in the framework of complex valued Schwartz distributions, where these equations were properly introduced in two different ways. The solution sets of these equations are, typically, exponential polynomials and, in some particular cases, they reduce to ordinary polynomials. In this paper we present several characterizations of or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00875","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":"1702.00875","created_at":"2026-05-18T00:51:29.538120+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.00875v1","created_at":"2026-05-18T00:51:29.538120+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00875","created_at":"2026-05-18T00:51:29.538120+00:00"},{"alias_kind":"pith_short_12","alias_value":"BO3Y4UEV36P5","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BO3Y4UEV36P5LGRR","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BO3Y4UEV","created_at":"2026-05-18T12:31:08.081275+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/BO3Y4UEV36P5LGRRNFFJSGZIWW","json":"https://pith.science/pith/BO3Y4UEV36P5LGRRNFFJSGZIWW.json","graph_json":"https://pith.science/api/pith-number/BO3Y4UEV36P5LGRRNFFJSGZIWW/graph.json","events_json":"https://pith.science/api/pith-number/BO3Y4UEV36P5LGRRNFFJSGZIWW/events.json","paper":"https://pith.science/paper/BO3Y4UEV"},"agent_actions":{"view_html":"https://pith.science/pith/BO3Y4UEV36P5LGRRNFFJSGZIWW","download_json":"https://pith.science/pith/BO3Y4UEV36P5LGRRNFFJSGZIWW.json","view_paper":"https://pith.science/paper/BO3Y4UEV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.00875&json=true","fetch_graph":"https://pith.science/api/pith-number/BO3Y4UEV36P5LGRRNFFJSGZIWW/graph.json","fetch_events":"https://pith.science/api/pith-number/BO3Y4UEV36P5LGRRNFFJSGZIWW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BO3Y4UEV36P5LGRRNFFJSGZIWW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BO3Y4UEV36P5LGRRNFFJSGZIWW/action/storage_attestation","attest_author":"https://pith.science/pith/BO3Y4UEV36P5LGRRNFFJSGZIWW/action/author_attestation","sign_citation":"https://pith.science/pith/BO3Y4UEV36P5LGRRNFFJSGZIWW/action/citation_signature","submit_replication":"https://pith.science/pith/BO3Y4UEV36P5LGRRNFFJSGZIWW/action/replication_record"}},"created_at":"2026-05-18T00:51:29.538120+00:00","updated_at":"2026-05-18T00:51:29.538120+00:00"}