{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:22:31Z","timestamp":1776795751276,"version":"3.51.2"},"reference-count":28,"publisher":"American Mathematical Society (AMS)","issue":"282","license":[{"start":{"date-parts":[[2013,11,28]],"date-time":"2013-11-28T00:00:00Z","timestamp":1385596800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper we consider transformations of sequences of orthogonal polynomials associated with a Hermitian linear functional\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper L\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">L<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathcal {L}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    using spectral transformations of the corresponding\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper C\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">C<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathcal {C}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -function\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper F Subscript script upper L\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>F<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">L<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">F_{\\mathcal {L}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We show that a rational spectral transformation of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper F Subscript script upper L\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>F<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">L<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">F_{\\mathcal {L}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with polynomial coefficients is a finite composition of four canonical spectral transformations.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2012-02655-x","type":"journal-article","created":{"date-parts":[[2012,11,28]],"date-time":"2012-11-28T08:23:25Z","timestamp":1354091005000},"page":"1057-1068","source":"Crossref","is-referenced-by-count":3,"title":["Generators of rational spectral transformations for nontrivial \ud835\udc9e-functions"],"prefix":"10.1090","volume":"82","author":[{"given":"Kenier","family":"Castillo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco","family":"Marcell\u00e1n","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2012,11,28]]},"reference":[{"issue":"8","key":"1","doi-asserted-by":"publisher","first-page":"988","DOI":"10.1016\/j.jat.2011.02.014","article-title":"Direct and inverse polynomial perturbations of Hermitian linear functionals","volume":"163","author":"Cantero, M. J.","year":"2011","journal-title":"J. Approx. Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9045","issn-type":"print"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/BF01449883","article-title":"\u00dcber den Variabilit\u00e4tsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen","volume":"64","author":"Carath\u00e9odory, C.","year":"1907","journal-title":"Math. Ann.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5831","issn-type":"print"},{"key":"3","doi-asserted-by":"crossref","unstructured":"K. Castillo, L. Garza, and F. Marcell\u00e1n, A new linear spectral transformation associated with derivatives of Dirac linear functionals, J. Approx. Theory 163 (2011), 1834\u20131853.","DOI":"10.1016\/j.jat.2011.08.003"},{"key":"4","first-page":"83","article-title":"Laurent polynomial perturbations of linear functionals. 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