Semigroups of bicomplex linear operators
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DOI:
https://doi.org/10.26637/MJM0802/0053Abstract
In this paper, we study bicomplex matrix-valued semigroups and also investigate uniformly continuous semigroups of linear operators with bicomplex scalars.
Keywords:
Matrix-valued semigroups, bicomplex modules, hyperbolic modules, bicomplex hermitian and skew-hermitian matrix, Functional Equation, one parameter semigroup, uniformly continuous operator semigroupsMathematics Subject Classification:
Mathematics- Pages: 633-641
- Date Published: 01-04-2020
- Vol. 8 No. 02 (2020): Malaya Journal of Matematik (MJM)
D. Alpay, M. E. Luna-Elizarrarás, M. Shapiro, D. C. Struppa, Basics of Functional Analysis with Bicomplex scalars and Bicomplex Schur Analysis, Springer Breifs in Mathematics, 2014.
F. Colombo, I. Sabadini and D. C. Struppa, Bicomplex holomorphic functional calculus, Math. Nachr., 287(13)(2013), 1093-1105.
J. B. Conway, A Course in Functional Analysis, 2nd Edition, Springer, Berlin, 1990.
N. Dunford and J. T. Schwartz Linear Operators, Part 1: General Theory, Interscience Publishers, New YorkLondon, 1958.
K. J .Engel and R. Nagel, One parameter semigroups for linear evolution equations, Graduate texts in Maths., Springer-Verlag, New York, 2000.
H. Gargoubi and S. Kossentini, f - Algebra Structure on Hyperbolic Numbers, Adv. Appl. Clifford Algebr., $26(2016), 1211-1233$.
R. Gervais Lavoie, L. Marchildon and D. Rochan, Finitedimensionalbicomplex Hilbert spaces, Adv.Appl. Clifford Algebr., 21(3)(2011), 561-581.
R. Gervais Lavoie, L. Marchildon and D. Rochan, Infinitedimensionalbicomplex Hilbert spaces, Ann. Funct. Anal., 1(2)(2010), 75-91.
E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer Verleg, New York, 1965.
R. Kumar, R. Kumar and D. Rochan, The fundamental theorems in the framework of bicomplex topological modules, (2011), arXiv:1109.3424v.1.
R. Kumar and H. Saini, Topological Bicomplex Modules, Adv. Appl. Clifford Algebr., 26(4)(2016), 1249-1270.
R. Kumar and K. Singh, Bicomplex linear operators on bicomplex Hilbert spaces and Littlewood's subordination theorem, Adv. Appl. Clifford Algebr., 25(3)(2015), 59196610.
R. Kumar, K. Singh, H. Saini and S. Kumar, Bicomplex weighted Hardy spaces and bicomplexC^*-algebras, Adv. Appl. Clifford Algebr., 26(1)(2016), 217-235.
M. E. Luna-Elizarrarás, M. Shapiro, D. C. Struppa and AVajiac, Bicomplex Holomorphic Functions :The Algebra, Geometry and Analysis, of BicomplexNymbers, Frontiers in Mathematics. Springer. New York. (2015).
M. E. Luna-Elizarrarás, M. Shapiro and D. C. Struppa, On Clifford analysis for holomorphic mappings, $A d v$. Geom., 14(3)(2014), 413-426.
M. E. Luna-Elizarrarás, M. Shapiro, D. C. Struppa and A-Vajiac, Bicomplex numbers and their elementary functions, Cubo, A mathematical Journal, 14(2)(2013), 61-80.
M. E. Luna-Elizarrarás, M. Shapiro, D. C. Struppa and A. Vajiac, Complex Laplacian and derivatives of bicomplex functions, Complex Anal. Oper. Theory, 7(2013), 16751711.
M. E. Luna-Elizarrarás, C. O. Perez-Regalado and M. Shapiro, On the Laurent series for bicomplex holomorphic functions, Complex Variables and Elliptic Eqn., $62(9)(2017), 1266-1286$.
M. E. Luna-Elizarrarás, C. O. Perez-Regalado and M. Shapiro, On the bicomplex Gleason-KahaneZelazko Theorem, Complex Anal. Oper. Theory, 10(2)(2016), 327352.
M. E. Luna-Elizarrarás, C .O. Perez-Regalado and M. Shapiro, On Linear functionals and Hahn-Banach theorems for hyperbolic and bicomplex-modules, Adv. Appl. Clifford Algebras, 24 (2014), 1105-1129.
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1986.
G. B. Price, An Introduction to Multicomplex Spaces and Functions, 3rd Edition, Marcel Dekker, New York, 1991.
D. Rochan and M. Shapiro, On algebraic properties of bicomplex and hyperbolic numbers, Anal. Univ. Oradea, Fasc. math., 11 (2004), 71-110.
D. Rochan and S. Tremblay, Bicomplex Quantum Me-chanics I: The Generalized Schrodinger Equation, $A d v$. App. Cliff. Algebr., 14(2)(2004), 231-248.
D. Rochan and S. Tremblay, Bicomplex Quantum Mechanics II: The Hilbert Space, Advances in Applied Clifford Algebras, 16(2)(2006), 135-157.
W. Rudin, Functional Analysis, 2nd Edition, McGraw Hill, New York, 1991.
H. Saini, A. Sharma and R. Kumar, Some fundamental results in functional analysis with bicomplex and hyperbolic scalars, (2018), arXiv:1510.01538v3, [math.FA].
C. Segre, Le rappresentazionirealidelleformecomplesse e glientiiperalgebrici, Math. Ann., 40(1892), 413-467.
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