Unconditionality of Periodic Orthonormal Spline Systems in $$\boldsymbol{H}^{\mathbf{1}}{(\mathbb{T})}$$: Necessity
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Published:2024-08
Issue:4
Volume:59
Page:245-261
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ISSN:1068-3623
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Container-title:Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)
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language:en
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Short-container-title:J. Contemp. Mathemat. Anal.
Reference24 articles.
1. G. Gevorkyan, A. Kamont, K. Keryan, and M. Passenbrunner, ‘‘Unconditionality of orthogonal spline systems in $$H^{1}[0,1]$$,’’ Stud. Math. 226, 123–154 (2015). https://doi.org/10.4064/2Fsm226-2-2
2. L. Hakobyan and K. Keryan, ‘‘Unconditionality of periodic orthonormal spline systems in $$H^{1}(\mathbb{T})$$: Sufficiency,’’ J. Contemp. Math. Anal. 59, 163–186 (2024). https://doi.org/10.3103/S1068362324700158
3. A. Yu. Shadrin, ‘‘The $$L_{\infty}$$-norm of the $$L_{2}$$-spline projector is bounded independently of the knot sequence: A proof of de Boor’s conjecture,’’ Acta Math. 187, 59–137 (2001). https://doi.org/10.1007/BF02392832
4. S. V. Bočkarev, ‘‘Some inequalities for Franklin series,’’ Anal. Math. 1, 249–257 (1975). https://doi.org/10.1007/BF02333175
5. Z. Ciesielski, ‘‘Equivalence, unconditionality and convergence a.e. of the spline bases in $$L_{p}$$ spaces,’’ Banach Center Publ. 4 (1), 55–68 (1975).