Gu, Cheng-Yang; Guo, Victor J. W. \(q\)-analogues of two supercongruences of Z.-W. Sun. (English) Zbl 07250687 Czech. Math. J. 70, No. 3, 757-765 (2020). MSC: 11B65 05A10 05A30 11A07 PDF BibTeX XML Cite \textit{C.-Y. Gu} and \textit{V. J. W. Guo}, Czech. Math. J. 70, No. 3, 757--765 (2020; Zbl 07250687) Full Text: DOI
Şayli, Mustafa; Lai, Yi Ming; Thul, Rüdiger; Coombes, Stephen Synchrony in networks of Franklin bells. (English) Zbl 1429.34060 IMA J. Appl. Math. 84, No. 5, 1001-1021 (2019). MSC: 34D06 34C15 34A36 34A37 92B20 PDF BibTeX XML Cite \textit{M. Şayli} et al., IMA J. Appl. Math. 84, No. 5, 1001--1021 (2019; Zbl 1429.34060) Full Text: DOI
Gevorkyan, G. G.; Keryan, K. A. On a system of piecewise linear functions with vanishing integrals on \(R\). (English. Russian original) Zbl 1355.42027 J. Contemp. Math. Anal., Armen. Acad. Sci. 51, No. 2, 68-78 (2016); translation from Izv. Nats. Akad. Nauk Armen., Mat. 51, No. 2, 3-16 (2016). Reviewer: Alexei Lukashov (Saratov) MSC: 42C05 46E30 PDF BibTeX XML Cite \textit{G. G. Gevorkyan} and \textit{K. A. Keryan}, J. Contemp. Math. Anal., Armen. Acad. Sci. 51, No. 2, 68--78 (2016; Zbl 1355.42027); translation from Izv. Nats. Akad. Nauk Armen., Mat. 51, No. 2, 3--16 (2016) Full Text: DOI
Meller, Magdalena; Jarzȩbkowska, Natalia Estimation of a smoothness parameter by spline wavelets. (English) Zbl 1381.62056 Appl. Math. 40, No. 3, 309-326 (2013). MSC: 62G05 42C40 65T60 PDF BibTeX XML Cite \textit{M. Meller} and \textit{N. Jarzȩbkowska}, Appl. Math. 40, No. 3, 309--326 (2013; Zbl 1381.62056) Full Text: DOI
Fukuda, N.; Kinoshita, T. On non-symmetric orthogonal spline wavelets. (English) Zbl 1274.42090 Southeast Asian Bull. Math. 36, No. 3, 319-341 (2012). MSC: 42C40 PDF BibTeX XML Cite \textit{N. Fukuda} and \textit{T. Kinoshita}, Southeast Asian Bull. Math. 36, No. 3, 319--341 (2012; Zbl 1274.42090)
Gevorkyan, Gegham G.; Kamont, Anna Orthonormal spline systems with arbitrary knots and bases in disk algebra. (English) Zbl 1260.41004 East J. Approx. 17, No. 4, 385-411 (2011). MSC: 41A15 42C05 PDF BibTeX XML Cite \textit{G. G. Gevorkyan} and \textit{A. Kamont}, East J. Approx. 17, No. 4, 385--411 (2011; Zbl 1260.41004)
Gevorkyan, Gegham; Kamont, Anna Uniqueness of series with respect to general Franklin systems. (English) Zbl 1178.42024 J. Contemp. Math. Anal., Armen. Acad. Sci. 44, No. 5, 271-283 (2009) and Izv. Nats. Akad. Nauk Armen., Mat. 44, No. 5, 3-18 (2009). MSC: 42C05 42C40 PDF BibTeX XML Cite \textit{G. Gevorkyan} and \textit{A. Kamont}, J. Contemp. Math. Anal., Armen. Acad. Sci. 44, No. 5, 271--283 (2009; Zbl 1178.42024) Full Text: DOI
Kyriazis, George; Park, Kyungwon; Petrushev, Pencho Anisotropic Franklin bases on polygonal domains. (English) Zbl 1096.42012 Math. Nachr. 279, No. 9-10, 1099-1127 (2006). MSC: 42C10 46E30 43A85 PDF BibTeX XML Cite \textit{G. Kyriazis} et al., Math. Nachr. 279, No. 9--10, 1099--1127 (2006; Zbl 1096.42012) Full Text: DOI
Petrushev, Pencho Anisotropic spaces and nonlinear \(n\)-term spline approximation. (English) Zbl 1085.41013 Chui, Charles K.(ed.) et al., Approximation theory XI. Proceedings of the 11th international conference, Gatlinburg, TN, USA, May 18–22, 2004. Brentwood, TN: Nashboro Press (ISBN 0-9728482-5-8/hbk). Modern Methods in Mathematics, 363-394 (2005). Reviewer: Martin D. Buhmann (Gießen) MSC: 41A30 41A15 42C15 PDF BibTeX XML Cite \textit{P. Petrushev}, in: Approximation theory XI. Proceedings of the 11th international conference, Gatlinburg, TN, USA, May 18--22, 2004. Brentwood, TN: Nashboro Press. 363--394 (2005; Zbl 1085.41013)
Privett, Roy F. The 2003 Benjamin Franklin Medal in Electrical Engineering presented to Bishnu S. Atal. (English) Zbl 1117.01307 J. Franklin Inst. 341, No. 3, 185-190 (2004). MSC: 01A70 93-03 PDF BibTeX XML Cite \textit{R. F. Privett}, J. Franklin Inst. 341, No. 3, 185--190 (2004; Zbl 1117.01307) Full Text: DOI
Ciesielski, Z.; Kamont, A. The Lebesgue constants for the Franklin orthogonal system. (English) Zbl 1056.42021 Stud. Math. 164, No. 1, 55-73 (2004). Reviewer: Ferenc Weisz (Budapest) MSC: 42C10 41A15 42C40 PDF BibTeX XML Cite \textit{Z. Ciesielski} and \textit{A. Kamont}, Stud. Math. 164, No. 1, 55--73 (2004; Zbl 1056.42021) Full Text: DOI
Schipp, Ferenc Orthogonal product systems of rational functions. (English) Zbl 1036.42028 Bojanov, B. D., Constructive theory of functions. Proceedings of the international conference, Varna, Bulgaria, June 19–23, 2002. Sofia: DARBA (ISBN 954-90126-6-2/hbk). 391-396 (2003). MSC: 42C10 PDF BibTeX XML Cite \textit{F. Schipp}, in: Constructive theory of functions. Proceedings of the international conference, Varna, Bulgaria, June 19--23, 2002. Sofia: DARBA. 391--396 (2003; Zbl 1036.42028)
Jonsson, Alf; Kamont, Anna Piecewise linear bases and Besov spaces on fractal sets. (English) Zbl 0994.46009 Anal. Math. 27, No. 2, 77-117 (2001). Reviewer: Joan Cerdà (Barcelona) MSC: 46E35 28A80 42C40 46B15 PDF BibTeX XML Cite \textit{A. Jonsson} and \textit{A. Kamont}, Anal. Math. 27, No. 2, 77--117 (2001; Zbl 0994.46009) Full Text: DOI
Gevorkyan, G. G.; Sahakian, A. A. Unconditional basis property of generalized Franklin systems. (English. Russian original) Zbl 1022.42020 J. Contemp. Math. Anal., Armen. Acad. Sci. 35, No. 4, 2-22 (2000); translation from Izv. Nats. Akad. Nauk Armen., Mat. 35, No. 4, 7-25 (2000). MSC: 42C10 46E30 PDF BibTeX XML Cite \textit{G. G. Gevorkyan} and \textit{A. A. Sahakian}, J. Contemp. Math. Anal., Armen. Acad. Sci. 35, No. 4, 2--22 (2000; Zbl 1022.42020); translation from Izv. Nats. Akad. Nauk Armen., Mat. 35, No. 4, 7--25 (2000)
Poghosyan, M. P. Almost everywhere convergence of series by generalized Franklin systems. (English. Russian original) Zbl 1022.42018 J. Contemp. Math. Anal., Armen. Acad. Sci. 35, No. 2, 61-73 (2000); translation from Izv. Nats. Akad. Nauk Armen., Mat. 35, No. 2, 64-77 (2000). MSC: 42C10 PDF BibTeX XML Cite \textit{M. P. Poghosyan}, J. Contemp. Math. Anal., Armen. Acad. Sci. 35, No. 2, 61--73 (2000; Zbl 1022.42018); translation from Izv. Nats. Akad. Nauk Armen., Mat. 35, No. 2, 64--77 (2000)
Karayannakis, D. Localization of the Franklin wavelets on the line. (English) Zbl 0962.42022 Int. J. Math. Game Theory Algebra 10, No. 4, 265-274 (2000). MSC: 42C40 PDF BibTeX XML Cite \textit{D. Karayannakis}, Int. J. Math. Game Theory Algebra 10, No. 4, 265--274 (2000; Zbl 0962.42022)
Magiropoulos, M. A nodal representation of the Franklin wavelets on the line. (English) Zbl 0962.42021 Int. J. Math. Game Theory Algebra 10, No. 4, 257-264 (2000). MSC: 42C40 PDF BibTeX XML Cite \textit{M. Magiropoulos}, Int. J. Math. Game Theory Algebra 10, No. 4, 257--264 (2000; Zbl 0962.42021)
Karayannakis, Dimitri On the nodal values of the Franklin analyzing wavelet. (English) Zbl 0848.65095 Chui, Charles K. (ed.) et al., Wavelets: theory, algorithms, and applications. Proceedings of the international conference on wavelets, held in Taormina, Italy, October 14-20, 1993. San Diego, CA: Academic Press. Wavelet Anal. Appl. 5, 449-458 (1994). MSC: 65T60 42C40 PDF BibTeX XML Cite \textit{D. Karayannakis}, in: Wavelets: theory, algorithms, and applications. Proceedings of the international conference on wavelets, held in Taormina, Italy, October 14-20, 1993. San Diego, CA: Academic Press. 449--458 (1994; Zbl 0848.65095)
Bochkarev, S. V. Series generated by Steklov functions. (English. Russian original) Zbl 0947.42019 Russ. Acad. Sci., Dokl., Math. 49, No. 1, 154-159 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 334, No. 5, 556-559 (1994). Reviewer: Khanlar P.Rustamov (MR 95m:42005) MSC: 42C10 26D15 46E35 PDF BibTeX XML Cite \textit{S. V. Bochkarev}, Russ. Acad. Sci., Dokl., Math. 49, No. 1, 154--159 (1994; Zbl 0947.42019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 334, No. 5, 556--559 (1994)
Kateb, Djalil; Drouiche, Karim The Strömberg wavelet and the Franklin system. (English) Zbl 0841.94013 IEEE Trans. Signal Process. 41, No. 12, 3562-3566 (1993). MSC: 94A12 42C40 PDF BibTeX XML Cite \textit{D. Kateb} and \textit{K. Drouiche}, IEEE Trans. Signal Process. 41, No. 12, 3562--3566 (1993; Zbl 0841.94013) Full Text: DOI
Müller, Paul F. X.; Schechtman, Gideon Several results concerning unconditionality in vector valued \(L^ p\) and \(H^ 1({\mathcal F}_ n)\) spaces. (English) Zbl 0723.46029 Ill. J. Math. 35, No. 2, 220-233 (1991). Reviewer: Yu Xin-tai (Shanghai) MSC: 46E40 46B15 46E30 46B20 42C20 42B30 PDF BibTeX XML Cite \textit{P. F. X. Müller} and \textit{G. Schechtman}, Ill. J. Math. 35, No. 2, 220--233 (1991; Zbl 0723.46029)
Kopaliani, T. S. On bases in \(L^{p(t)} ([0,1]^ n)\) space. (Russian. English, Georgian summaries) Zbl 0769.46019 Soobshch. Akad. Nauk Gruz. SSR 142, No. 1, 21-23 (1991). MSC: 46E30 46B15 PDF BibTeX XML Cite \textit{T. S. Kopaliani}, Soobshch. Akad. Nauk Gruz. SSR 142, No. 1, 21--23 (1991; Zbl 0769.46019)
Kazaryan, K. S.; Sargsyan, A. S. Divergence almost everywhere of Fourier-Ciesielski series. (English. Russian original) Zbl 0715.42023 Sov. J. Contemp. Math. Anal., Arm. Acad. Sci. 24, No. 4, 91-99 (1989); translation from Izv. Akad. Nauk Arm. SSR, Mat. 24, No. 4, 403-412 (1989). MSC: 42C10 42C30 PDF BibTeX XML Cite \textit{K. S. Kazaryan} and \textit{A. S. Sargsyan}, Sov. J. Contemp. Math. Anal., Arm. Acad. Sci. 24, No. 4, 91--99 (1989; Zbl 0715.42023); translation from Izv. Akad. Nauk Arm. SSR, Mat. 24, No. 4, 403--412 (1989)
Meyer, Yves Wavelets and operators. (English) Zbl 0704.46008 Analysis at Urbana. Vol. 1: Analysis in function spaces, Proc. Spec. Year Mod. Anal./Ill. 1986-87, Lond. Math. Soc. Lect. Note Ser. 137, 256-365 (1989). Reviewer: M.Ostrovskij MSC: 46B15 42C40 47B38 PDF BibTeX XML
Kazaryan, K. S.; Sargsyan, A. S. Divergence almost everywhere of Fourier series with respect to the Ciesielski system. (Russian. English summary) Zbl 0686.42021 Izv. Akad. Nauk Arm. SSR, Mat. 24, No. 4, 403-412 (1989). MSC: 42C15 42A20 PDF BibTeX XML Cite \textit{K. S. Kazaryan} and \textit{A. S. Sargsyan}, Izv. Akad. Nauk Arm. SSR, Mat. 24, No. 4, 403--412 (1989; Zbl 0686.42021)
Meyer, Yves Ondelettes, filtres miroirs en quadrature et traitement numérique de l’image. (Wavelets, quadratic mirror filters and numerical treatment of the image). (French) Zbl 0674.42011 Gaz. Math., Soc. Math. Fr. 40, 31-42 (1989). Reviewer: W.Luther MSC: 42C40 33C45 PDF BibTeX XML Cite \textit{Y. Meyer}, Gaz. Math., Soc. Math. Fr. 40, 31--42 (1989; Zbl 0674.42011)
Kashin, B. S.; Saakyan, A. A. Orthogonal series. Transl. from the Russian by Ralph P. Boas. Transl. ed. by Ben Silver. (English) Zbl 0668.42011 Translations of Mathematical Monographs, 75. Providence, RI: American Mathematical Society (AMS). xii, 451 p. $ 146.00 (1989). MSC: 42C05 42-02 42A38 42A20 PDF BibTeX XML Cite \textit{B. S. Kashin} and \textit{A. A. Saakyan}, Orthogonal series. Transl. from the Russian by Ralph P. Boas. Transl. ed. by Ben Silver. Providence, RI: American Mathematical Society (1989; Zbl 0668.42011)
Tkebuchava, G. E. On multiple function systems in Orlicz spaces. (Russian. English summary) Zbl 0694.42028 Soobshch. Akad. Nauk Gruz. SSR 129, No. 2, 249-252 (1988). MSC: 42C30 42C15 PDF BibTeX XML Cite \textit{G. E. Tkebuchava}, Soobshch. Akad. Nauk Gruz. SSR 129, No. 2, 249--252 (1988; Zbl 0694.42028)
Berkson, E. On the decay properties of the Franklin analyzing wavelet. (English) Zbl 0675.42021 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 5, No. 5, 409-424 (1988). Reviewer: W.Luther MSC: 42C40 33C45 PDF BibTeX XML Cite \textit{E. Berkson}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 5, No. 5, 409--424 (1988; Zbl 0675.42021) Full Text: DOI Numdam EuDML
Wronicz, Zygmunt Systems conjugate to biorthogonal spline systems. (English) Zbl 0777.46012 Bull. Pol. Acad. Sci., Math. 36, No. 5-6, 279-288 (1988). Reviewer: N.Bozhinov (Sofia) MSC: 46B15 46C15 41A30 PDF BibTeX XML Cite \textit{Z. Wronicz}, Bull. Pol. Acad. Sci., Math. 36, No. 5--6, 279--288 (1988; Zbl 0777.46012)
Kashin, B. S.; Saakyan, A. A. Orthogonal series. (Ортогональные ряды.) (Russian) Zbl 0632.42017 Moskva: Nauka. 496 p. R. 4.10 (1984). MSC: 42C05 42-02 42A38 42A20 PDF BibTeX XML
Strömberg, Jan-Olov A modified Franklin system and higher-order spline systems on \(\mathbb R^ n\) as unconditional bases for Hardy spaces. (English) Zbl 0521.46011 Harmonic analysis, Conf. in Honor A. Zygmund, Chicago 1981, Vol. 2, 475-494 (1983). Reviewer: S. Cobzaş MSC: 46B15 46J15 42B30 PDF BibTeX XML
Sjoelin, Per; Strömberg, Jan-Olov Basis properties of Hardy spaces. (English) Zbl 0519.46058 Ark. Mat. 21, 111-125 (1983). MSC: 46J15 42C10 46B15 41A15 PDF BibTeX XML Cite \textit{P. Sjoelin} and \textit{J.-O. Strömberg}, Ark. Mat. 21, 111--125 (1983; Zbl 0519.46058) Full Text: DOI
Hsu, Naihung Best approximation by Franklin polynomials. (English) Zbl 0528.41014 Tamkang J. Math. 13, 247-254 (1982). MSC: 41A50 41A30 41A10 41A25 PDF BibTeX XML Cite \textit{N. Hsu}, Tamkang J. Math. 13, 247--254 (1982; Zbl 0528.41014)
Oswald, P. On spline bases in periodic Hardy spaces (\(0< p\leq 1\)). (English) Zbl 0519.46056 Math. Nachr. 108, 219-229 (1982). MSC: 46J15 46B15 41A15 42B30 42C30 PDF BibTeX XML Cite \textit{P. Oswald}, Math. Nachr. 108, 219--229 (1982; Zbl 0519.46056) Full Text: DOI
Komissarov, A. A. Equivalence of the Haar and Franklin systems in certain function spaces. (English. Russian original) Zbl 0508.46017 Sib. Math. J. 23, 681-690 (1983); translation from Sib. Mat. Zh. 23, No. 5, 115-126 (1982). MSC: 46E30 46B15 PDF BibTeX XML Cite \textit{A. A. Komissarov}, Sib. Math. J. 23, 681--690 (1982; Zbl 0508.46017); translation from Sib. Mat. Zh. 23, No. 5, 115--126 (1982) Full Text: DOI
Tsagarejshvili, V. Sh. Absolute convergence of orthogonal Fourier series. (Russian) Zbl 0489.42031 Some questions of function theory, Vol. 2, Work Collect., Tbilisi 1981, 93-109 (1981). MSC: 42C10 42A20 PDF BibTeX XML
Bashkirov, A. I. On maximal almost disjoint systems and Franklin bicompacta. (English. Russian original) Zbl 0416.54017 Sov. Math., Dokl. 19, 864-868 (1978); translation from Dokl. Akad. Nauk SSSR 241, 509-512 (1978). MSC: 54D30 54A35 PDF BibTeX XML Cite \textit{A. I. Bashkirov}, Sov. Math., Dokl. 19, 864--868 (1978; Zbl 0416.54017); translation from Dokl. Akad. Nauk SSSR 241, 509--512 (1978)