An extension of the complex–real (C–R) calculus to the bicomplex setting, with applications
In this paper, we extend notions of complex C−R$\mathbb {C} - \mathbb {R}$‐calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical re...
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| Veröffentlicht in: | Mathematische Nachrichten Jg. 297; H. 2; S. 454 - 481 |
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| Abstract | In this paper, we extend notions of complex C−R$\mathbb {C} - \mathbb {R}$‐calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms. |
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| AbstractList | In this paper, we extend notions of complex ‐calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms. In this paper, we extend notions of complex C−R$\mathbb {C} - \mathbb {R}$‐calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms. In this paper, we extend notions of complex C−R$\mathbb {C} - \mathbb {R}$‐calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms. |
| Author | Alpay, Daniel Vajiac, Mihaela Diki, Kamal |
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| References | 1927; 97 2012; 285 1987; 75 1983; 130 2022; 94 2021; 423 1997; 85 2009 2007 2023; 445 1974 2005 2016; 744 2011; 56 1991 1892; 40 2011; 18 1952; 22 2009; 57 1991; 140 2023 2020; 53 2022 1995; 26 260 1958; 65 2018 2017 2016 2015 1960 1975; 63 2014 2011; 49 2012; 23 e_1_2_8_29_1 e_1_2_8_24_1 e_1_2_8_25_1 e_1_2_8_26_1 e_1_2_8_27_1 Vajiac A. (e_1_2_8_34_1) 2011; 56 e_1_2_8_3_1 e_1_2_8_2_1 e_1_2_8_5_1 Balk M. B. (e_1_2_8_10_1) 1991 e_1_2_8_4_1 e_1_2_8_7_1 e_1_2_8_9_1 e_1_2_8_8_1 e_1_2_8_20_1 e_1_2_8_21_1 e_1_2_8_22_1 e_1_2_8_23_1 e_1_2_8_17_1 e_1_2_8_18_1 e_1_2_8_19_1 e_1_2_8_13_1 e_1_2_8_36_1 e_1_2_8_14_1 e_1_2_8_35_1 e_1_2_8_15_1 e_1_2_8_38_1 e_1_2_8_16_1 e_1_2_8_37_1 Price G. B. (e_1_2_8_28_1) 1991 e_1_2_8_32_1 e_1_2_8_31_1 e_1_2_8_11_1 e_1_2_8_12_1 e_1_2_8_33_1 Alpay D. (e_1_2_8_6_1) 2023; 445 e_1_2_8_30_1 |
| References_xml | – year: 2009 – volume: 53 start-page: 2957 issue: 4 year: 2020 end-page: 2982 article-title: Survey of quaternion neural networks publication-title: Artif. Intell. Rev. – volume: 130 start-page: 11 year: 1983 end-page: 16 article-title: A complex gradient operator and its application in adaptive array theory publication-title: IEE Proc. H: Microwaves Optics Antennas – volume: 423 start-page: 80 year: 2021 end-page: 88 article-title: Synthesis of complex‐and hyperbolic‐valued Hopfield neural networks publication-title: Neurocomputing – year: 2005 – volume: 85 start-page: 195 year: 1997 end-page: 253 – year: 2007 – volume: 445 start-page: 12 year: 2023 article-title: A note on the complex and bicomplex valued neural networks publication-title: Appl. Math. Comput. – volume: 423 start-page: 535 year: 2021 end-page: 540 article-title: Complex‐valued Hopfield neural networks with real weights in synchronous mode publication-title: Neurocomputing – volume: 57 start-page: 1316 issue: 4 year: 2009 end-page: 1327 article-title: The quaternion LMS algorithm for adaptive filtering of hypercomplex processes publication-title: IEEE Trans. Signal Process. – volume: 40 start-page: 413 year: 1892 end-page: 467 article-title: Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici publication-title: Math. Ann. – volume: 285 start-page: 1230 issue: 10 year: 2012 end-page: 1242 article-title: The Cauchy–Kowalewski product for bicomplex holomorphic functions publication-title: Math. Nachr. – year: 2016 – volume: 22 start-page: 63 year: 1952 end-page: 86 article-title: Complex multiple Wiener integral publication-title: Jap. J. Math – year: 2018 – start-page: 96 year: 1960 end-page: 104 article-title: Adaptive switching circuits – year: 2014 – volume: 49 start-page: 277 issue: 2 year: 2011 end-page: 294 article-title: Singularities of functions of one and several bicomplex variables publication-title: Ark. Mat. – volume: 744 year: 2016 article-title: CR‐Calculus and adaptive array theory applied to MIMO random vibrations control tests publication-title: J. Phys. Conf. Ser. – volume: 140 year: 1991 – volume: 63 start-page: 719 year: 1975 end-page: 720 article-title: The complex LMS algorithm publication-title: Proc. IEEE. – volume: 65 start-page: 386 issue: 6 year: 1958 end-page: 408 article-title: The perceptron: a probabilistic model for information storage and organization in the brain publication-title: Psychol. Rev. – volume: 26 start-page: 268 issue: 4 year: 1995 end-page: 280 article-title: The hyperbolic number plane publication-title: Coll. Math. J. – volume: 56 start-page: 1 issue: 12 year: 2011 end-page: 13 article-title: Multicomplex hyperfunctions publication-title: Complex Var. Elliptic Equ. – volume: 94 start-page: 35 year: 2022 article-title: Reproducing kernel hilbert spaces of polyanalytic functions of infinite order publication-title: Integr. Equ. Oper. Theory – year: 2022 – year: 2023 – volume: 23 start-page: 541 year: 2012 end-page: 551 article-title: Generalization characteristics of complex‐ valued feedforward neural networks in relation to signal coherence publication-title: IEEE Trans. Neural Netw. Learn. Syst. – volume: 75 start-page: 92 year: 1987 end-page: 127 article-title: Eigenvalue problems for the Schrödinger operator with the magnetic field on a compact Riemannian maniforld publication-title: J. Funct. Anal. – year: 1991 – volume: 18 start-page: 47 issue: 1 year: 2011 end-page: 50 article-title: A quaternion gradient operator and its applications publication-title: IEEE Signal Process. Lett. – start-page: 281 year: 2017 end-page: 299 article-title: Bernstein‐type inequalities for bicomplex polynomials – volume: 260 article-title: Norms and moduli on multicomplex spaces – year: 2015 – volume: 97 start-page: 357 year: 1927 end-page: 375 article-title: Zur formalen theorie der funktionen von mehr komplexen veranderlichen publication-title: Math. Annal. – year: 1974 article-title: Recueil de problémes sur la théorie des fonctions analytiques – ident: e_1_2_8_13_1 doi: 10.1007/s11512-010-0126-0 – ident: e_1_2_8_37_1 doi: 10.21236/AD0241531 – ident: e_1_2_8_4_1 doi: 10.1007/978-3-319-42181-0 – ident: e_1_2_8_20_1 doi: 10.1016/j.neucom.2020.10.072 – ident: e_1_2_8_9_1 doi: 10.1007/978-3-319-05110-9 – ident: e_1_2_8_21_1 doi: 10.1016/j.neucom.2020.10.002 – ident: e_1_2_8_26_1 doi: 10.1007/s10462-019-09752-1 – ident: e_1_2_8_30_1 doi: 10.1007/978-3-319-62362-7_11 – ident: e_1_2_8_3_1 – ident: e_1_2_8_22_1 – ident: e_1_2_8_38_1 doi: 10.1109/PROC.1975.9807 – volume-title: Polyanalytic functions year: 1991 ident: e_1_2_8_10_1 – ident: e_1_2_8_23_1 doi: 10.1007/978-3-319-24868-4 – ident: e_1_2_8_33_1 doi: 10.1080/07468342.1995.11973712 – volume-title: Monographs and Textbooks in Pure and Applied Mathematics year: 1991 ident: e_1_2_8_28_1 – ident: e_1_2_8_15_1 doi: 10.1007/s11785-022-01240-9 – ident: e_1_2_8_25_1 doi: 10.1088/1742-6596/744/1/012175 – ident: e_1_2_8_18_1 doi: 10.4099/jjm1924.22.0_63 – ident: e_1_2_8_7_1 – ident: e_1_2_8_17_1 doi: 10.1109/TNNLS.2012.2183613 – ident: e_1_2_8_32_1 doi: 10.1016/0022-1236(87)90108-X – ident: e_1_2_8_19_1 doi: 10.1109/LSP.2010.2091126 – ident: e_1_2_8_27_1 – volume: 445 start-page: 12 year: 2023 ident: e_1_2_8_6_1 article-title: A note on the complex and bicomplex valued neural networks publication-title: Appl. Math. Comput. – ident: e_1_2_8_16_1 – ident: e_1_2_8_31_1 doi: 10.1007/BF01443559 – ident: e_1_2_8_35_1 – ident: e_1_2_8_11_1 doi: 10.1007/978-3-662-03396-8_2 – ident: e_1_2_8_8_1 – volume: 56 start-page: 1 issue: 12 year: 2011 ident: e_1_2_8_34_1 article-title: Multicomplex hyperfunctions publication-title: Complex Var. Elliptic Equ. – ident: e_1_2_8_29_1 doi: 10.1037/h0042519 – ident: e_1_2_8_36_1 doi: 10.1007/BF01447872 – ident: e_1_2_8_12_1 doi: 10.1049/ip-h-1.1983.0004 – ident: e_1_2_8_5_1 doi: 10.1007/s00020-022-02713-4 – ident: e_1_2_8_24_1 doi: 10.1109/TSP.2008.2010600 – ident: e_1_2_8_14_1 doi: 10.1002/mana.201100047 – ident: e_1_2_8_2_1 doi: 10.1109/EURCON.2005.1629866 |
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| SubjectTerms | Algorithms BC−R$\mathbb {BC}-\mathbb {R}$ calculus bicomplex gradient operator bicomplex numbers BLMS algorithm C–R calculus |
| Title | An extension of the complex–real (C–R) calculus to the bicomplex setting, with applications |
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