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Approximation in weighted spaces of vector functions

Year 2021, Volume: 4 Issue: 2, 242 - 252, 01.06.2021
https://doi.org/10.33205/cma.825986

Abstract

In this paper, we present the duality theory for general weighted space of vector functions. We mention that a characterization of the dual of a weighted space of vector functions in the particular case $V \subset C^{+} (X)$ is mentioned by J. B. Prolla in [6]. Also, we extend de Branges lemma in this new setting for convex cones of a weighted spaces of vector functions (Theorem 4.2). Using this theorem, we find various approximations results for weighted spaces of vector functions: Theorems 4.2-4.6 as well as Corollary 4.3. We mention also that a brief version of this paper, in the particular case $V \subset C^{+} (X)$, is presented in [3], Chapter 2, subparagraph 2.5.

References

  • L. De Branges: The Stone-Weierstrass theorem, Proc. Amer. Math. Soc., 10 (5) (1959), 822–824.
  • I. Bucur, G. Pâltineanu: De Branges type lemma and approximation in weighted spaces, Mediterranean J. Math., (to appear).
  • I. Bucur, G. Pâltineanu: Topics in the uniform approximation of continuous functions, Birkhauser (2020).
  • L. Nachbin: Weigthed approximation for algebras and modules of continuous functions: real and self-adjoint complex cases, Ann. of Math., 81 (1965), 289–302.
  • L. Nachbin: Elements of approximation theory, D. Van Nostrand, Princeton (1967).
  • J. B. Prolla: Bishop’s generalized Stone-Weierstrass theorem for weighted spaces, Math. Anal., 191 (4) (1971), 283–289.
  • W. H. Summers: Dual spaces of weighted spaces, Trans. Amer. Math. Soc., 151 (1) (1970), 323–333.
Year 2021, Volume: 4 Issue: 2, 242 - 252, 01.06.2021
https://doi.org/10.33205/cma.825986

Abstract

References

  • L. De Branges: The Stone-Weierstrass theorem, Proc. Amer. Math. Soc., 10 (5) (1959), 822–824.
  • I. Bucur, G. Pâltineanu: De Branges type lemma and approximation in weighted spaces, Mediterranean J. Math., (to appear).
  • I. Bucur, G. Pâltineanu: Topics in the uniform approximation of continuous functions, Birkhauser (2020).
  • L. Nachbin: Weigthed approximation for algebras and modules of continuous functions: real and self-adjoint complex cases, Ann. of Math., 81 (1965), 289–302.
  • L. Nachbin: Elements of approximation theory, D. Van Nostrand, Princeton (1967).
  • J. B. Prolla: Bishop’s generalized Stone-Weierstrass theorem for weighted spaces, Math. Anal., 191 (4) (1971), 283–289.
  • W. H. Summers: Dual spaces of weighted spaces, Trans. Amer. Math. Soc., 151 (1) (1970), 323–333.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Gavriil Paltıneanu 0000-0002-9274-2727

Ileana Bucur 0000-0001-7832-7087

Publication Date June 1, 2021
Published in Issue Year 2021 Volume: 4 Issue: 2

Cite

APA Paltıneanu, G., & Bucur, I. (2021). Approximation in weighted spaces of vector functions. Constructive Mathematical Analysis, 4(2), 242-252. https://doi.org/10.33205/cma.825986
AMA Paltıneanu G, Bucur I. Approximation in weighted spaces of vector functions. CMA. June 2021;4(2):242-252. doi:10.33205/cma.825986
Chicago Paltıneanu, Gavriil, and Ileana Bucur. “Approximation in Weighted Spaces of Vector Functions”. Constructive Mathematical Analysis 4, no. 2 (June 2021): 242-52. https://doi.org/10.33205/cma.825986.
EndNote Paltıneanu G, Bucur I (June 1, 2021) Approximation in weighted spaces of vector functions. Constructive Mathematical Analysis 4 2 242–252.
IEEE G. Paltıneanu and I. Bucur, “Approximation in weighted spaces of vector functions”, CMA, vol. 4, no. 2, pp. 242–252, 2021, doi: 10.33205/cma.825986.
ISNAD Paltıneanu, Gavriil - Bucur, Ileana. “Approximation in Weighted Spaces of Vector Functions”. Constructive Mathematical Analysis 4/2 (June 2021), 242-252. https://doi.org/10.33205/cma.825986.
JAMA Paltıneanu G, Bucur I. Approximation in weighted spaces of vector functions. CMA. 2021;4:242–252.
MLA Paltıneanu, Gavriil and Ileana Bucur. “Approximation in Weighted Spaces of Vector Functions”. Constructive Mathematical Analysis, vol. 4, no. 2, 2021, pp. 242-5, doi:10.33205/cma.825986.
Vancouver Paltıneanu G, Bucur I. Approximation in weighted spaces of vector functions. CMA. 2021;4(2):242-5.