ORIGINAL_ARTICLE
Characterizations of amenable hypergroups
Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^\infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^\infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.
https://wala.vru.ac.ir/article_23365_e3e911df58170eb14ba5a4a8f162ef0c.pdf
2017-08-01
1
9
10.22072/wala.2017.23365
Amenability
Banach algebras
Hypergroup algebras
Left invariant mean
Topologically left invariant mean
Ali
Ghaffari
aghaffari@semnan.ac.ir
1
Semnan University
LEAD_AUTHOR
Mohammad Bagher
Sahabi
b_sahabi@yahoo.com
2
Payame Noor University
AUTHOR
[1] A. Azimifard, the alpha-amenability of hypergroups, Monatsh. Math., 155(1) (2008), 1-13.
1
[2] W.R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, vol. 20, de Gruyter Studies in Mathematics, Walter de Gruyter & Co., Berlin, 1995.
2
[3] C.F. Dunkl, The measure algebra of a locally compact hypergroup, Trans. Am. Math. Soc., 179 (1973), 331-348.
3
[4] R.E. Edwards, Functional Analysis, New-York, Holt, Rinehart and Winston, 1965.
4
[5] E.E. Granirer, Criteria for compactness and for discreteness of locally compact amenable groups, Proc. Am. Math. Soc., 40(2) (1973), 615-624.
5
[6] Z. Hu, M. Sangani Monfared and T. Traynor, On character amenable Banach algebras, Stud. Math., 193(1) (2009), 53-78.
6
[7] R.I. Jewett, Spaces with an abstract convolution of measures, Adv. Math., 18(1) (1975), 1-101.
7
[8] R.A. Kamyabi-Gol, Topological Center of Dual Banach Algebras Associated to Hypergroups, Ph.D. Thesis,
8
University of Alberta, 1997.
9
[9] R.A. Kamyabi-Gol, $P$-amenable locally compact hypergroups, Bull. Iran. Math. Soc., 32(2) (2006), 43-51.
10
[10] Lasser, Amenability and weak amenability of $l^1$-algebras of polynomial hypergroups, Stud. Math., 182(2) (2007), 183-196.
11
[11] A.R. Medghalchi, The second dual of a hypergroup, Math. Z., 210 (1992), 615-624.
12
[12] M.S. Monfared, Character amenability of Banach algebras, Math. Proc. Camb. Philos. Soc., 144(3) (2008), 697-706.
13
[13] W. Rudin, Functional Analysis, McGraw Hill, New York, 1991.
14
[14] M. Skantharajah, Amenable hypergroups, Illinois J. Math., 36(1) (1992), 15-46.
15
[15] R. Spector, Mesures invariantes sur les hypergroupes (French, with English summary), Trans. Am. Math. Soc., 239 (1978), 147-165.
16
[16] N. Tahmasebi, Hypergroups and invariant complemented subspaces, J. Math. Anal. Appl., 414 (2014), 641-651.
17
[17] B. Wilson, Configurations and invariant nets for amenable hypergroups and related algebras, Trans. Am. Math. Soc., 366(10) (2014), 5087-5112.
18
ORIGINAL_ARTICLE
Determination of subrepresentations of the standard higher dimensional shearlet group
This paper is devoted to definition standard higher dimension shearlet group $ \mathbb{S} = \mathbb{R}^{+} \times \mathbb {R}^{n-1} \times \mathbb {R}^{n} $ and determination of square integrable subrepresentations of this group. Also we give a characterisation of admissible vectors associated to the Hilbert spaces corresponding to each su brepresentations.
https://wala.vru.ac.ir/article_23366_278253b8ba374cbd231b1cdf2dd51313.pdf
2017-08-01
11
21
10.22072/wala.2017.23366
orbit
standard higher dimensional shearlet group
square-integrable representation
Masoumeh
zare
zare.masume@gmail.com
1
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran.
LEAD_AUTHOR
Rajab ali
Kamyabi-Gol
kamyabi@um.ac.ir
2
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran.
AUTHOR
Zahra
amiri
za_am10@stu.um.ac.ir
3
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran.
AUTHOR
[1] S.T. Ali, J.P. Antoine and J.P. Gazeau, Coherent States, Wavelets and Their Generalizations, New York: Springer-Verlag, 2000.
1
[2] A.A. Arefijamaal and R.A. Kamyabi-Gol, A characterization of square-integrable representations associated with CWT, J. Sci., Islam. Repub. Iran, 18(2) (2007), 159-166.
2
[3] V. Atayi and R.A. Kamyabi-Gol, On the characterization of subrepresentations of shearlet group, Wavelets and Linear Algebra, 2(1) (2015), 1-9.
3
[4] D. Bernier and K.F. Taylor, Wavelet from square-integrable representation, SIAM J. Math. Anal., 27(2) (1996), 594-608.
4
[5] E.J. Candes and D.L. Donoho, Curvelets: A surprisingly effective nonadaptive representation for objects with edges, Saint-Malo Proceedings, 2000.
5
[6] E.J. Candes and D.L. Donoho, Ridgelets: a key to higher-dimensional intermittency, Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci., 357(1760) (1999), 2495-2509.
6
[7] S. Dahlke, G. Kutyniok, C. Sagiv, H.G. Stark and G. Teschke, The uncertainty principle associated with the continuous shearlet transform, Int. J. Wavelets Multiresolut. Inf. Process., 6(2) (2008), 157-181.
7
[8] S. Dahlke and G. Teschke, The continuous shearlet transform in arbitrary space dimensions, J. Fourier Anal. Appl., 16 (2010), 340-364.
8
[9] M.N. Do and M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, IEEE Trans. Image Process., 14(12) (2005), 2091-2106.
9
[10] G.B. Folland, A Course in Abstract Harmonic Analysis, Boca Katon: CRC Press, 1995.
10
[11] K. Guo and D. Labate, Optimally sparse multidimensional representation using shearlets, SIAM J. Math. Anal., 39(1) (2007), 298-318.
11
[12] K. Guo, G. Kutyniok and D. Labate, Sparse multidimensional representations using anisotropic dilation and shear operators, International Conference on the Interaction between Wavelets and Splines, Athens, 2005.
12
[13] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, vol. 1, Springer-Verlag, Berlin, 1963.
13
[14] G. Kutyniok and W. Lim, Compactly Supported Shearlets, vol. 13, Approximation Theory XIII: San Antonio 2010. Springer Proceedings in Mathematics, Springer, New York, 2011.
14
[15] G. Kutyniok, W. Lim and X. Zhuang, Digital shearlet transforms, Appl. Comput. Harmon. Anal., (2012), 239--282.
15
[16] D. Labate, W. Lim, G. Kutyniok and G. Weiss, Sparse multidimensional representation using shearlets, SPIE Proc. 5914, SPIE, Bellingham, (2005), 254-262.
16
ORIGINAL_ARTICLE
On higher rank numerical hulls of normal matrices
In this paper, some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated. A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given. Moreover, using the extreme points of the numerical range, the higher rank numerical hulls of matrices of the form $A_1 \oplus i A_2$, where $A_1$ and $A_2$ are Hermitian, are investigated. The higher rank numerical hulls of the basic circulant matrix are also studied.
https://wala.vru.ac.ir/article_23367_ebbd946a37c2e6eee2b03af2d07bdd99.pdf
2017-08-01
23
32
10.22072/wala.2017.47123.1080
Rank-k numerical hulls
Joint rank-k numerical range
Polynomial numerical hull
basic circulant matrix
Golamreza
Aghamollaei
aghamollaei@uk.ac.ir
1
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Islamic Republic of Iran
LEAD_AUTHOR
Sharifeh
Rezagholi
sh_rezagholi79@yahoo.com
2
Department of Mathematics, Payame Noor University (PNU) ;Tehran; Islamic Republic of Iran.
AUTHOR
[1] H. Afshin, M. Mehrjoofard and A. Salemi, Polynomial numerical hulls of order 3, Electron. J. Linear Algebra, 18 (2009), 253-263.
1
[2] Gh. Aghamollaei and Sh. Rezagholi, Higher rank numerical hulls of matrices and matrix polynomials, Oper. Matrices, 9 (2015), 417-431.
2
[3] Gh. Aghamollaei and A. Salemi, Polynomial numerical hulls of matrix polynomials, II, Linear Multilinear Algebra, 59 (2011), 291-302.
3
[4] Ch. Davis, C.K. Li and A. Salemi, Polynomial numerical hulls of matrices, Linear Algebra Appl., 428 (2008), 137-153.
4
[5] Ch. Davis and A. Salemi, On polynomial numerical hulls of normal matrices, Linear Algebra Appl., 383 (2004), 151-161.
5
[6] H.L. Gau, C.H. Li, Y.T. Poon and N.S. Sze, Higher rank numerical ranges of normal matrices, SIAM J. Matrix Anal. Appl., 32 (2011), 23-43.
6
[7] A. Greenbaum, Generalizations of field of values useful in the study of polynomial functions of a matrix, Linear Algebra Appl., 347 (2002), 233-249.
7
[8] K.E. Gustafson amd D.K.M. Rao, Numerical Range: The Field of Values of Linear Operators and Matrices, Springer-Verlage, New York, 1997.
8
[9] R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, New York, 1991.
9
[10] C.K. Li and N.S. Sze, Canonical forms, higher-rank numerical ranges, totally isotropic subspaces, and matrix equations, Proc. Am. Math. Soc., 136(9) (2008), 3013-3023.
10
[11] O. Nevanlinna, Convergence of Iterations for Linear Equations, Birkhauser, Basel, 1993.
11
[12] M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, New York, 2010.
12
[13] A. Salemi, Higher rank numerical hulls of matrices, Oper. Matrices, 6 (2012), 79-84.
13
ORIGINAL_ARTICLE
A-B-imprimitivity bimodule frames
Frames in Hilbert bimodules are a special case of frames in Hilbert C*-modules. The paper considers A-frames and B-frames and their relationship in a Hilbert A-B-imprimitivity bimodule. Also, it is given that every frame in Hilbert spaces or Hilbert C*-modules is a semi-tight frame. A relation between A-frames and K(H_B)-frames is obtained in a Hilbert A-B-imprimitivity bimodule. Moreover, the last part of the paper investigates dual of an A-frame and a B-frame and presents a common property for all duals of a frame in a Hilbert A-B-imprimitivity bimodule.
https://wala.vru.ac.ir/article_25011_27d211d588301e528d336de1c9906af6.pdf
2017-08-01
33
41
10.22072/wala.2017.47173.1081
A-B-imprimitivity bimodule Frame
Frame
Hilbert A-B-imprimitivity bimodule
Semi-tight frame
Azadeh
Alijani
a_aligany@yahoo.com
1
Vali-e-Asr University of Rafsanjan
LEAD_AUTHOR
[1] A. Alijani, Dilations of *-Frames and their operator Duals, Preprint.
1
[2] A. Alijani and M.A. Dehghan, *-Frames in Hilbert C^*-modules, U.P.B. Sci. Bull., Ser. A, 73(4) (2011), 89-106.
2
[3] P. Casazza, D. Han and D. Larson, Frames for Banach spaces, Contemp. Math., 247 (1999), 149-181.
3
[4] P.G. Casazza and G. Kutyniok, Frames of subspaces, Contemp. Math., 345 (2004), 87-113.
4
[5] M. Frank and D.R. Larson, Frames in Hilbert C^*-modules and C^*-algebra, J. Oper. Theory, 48 (2002), 273-314.
5
[6] E.C. Lance, Hilbert $C^*$-modules, A Toolkit for Operator Algebraists, University of Leeds, Cambridge University Press}, 1995.
6
[7] G.J. Morphy, C^*-Algebras and Operator Theory, San Diego, California, Academic Press, 1990.
7
[8] L. Raeburn and D.P. Williams, Morita Equivalence and Continuous-Trace C^*-Algebras, Matemathical Surveys and Monographs, 1998.
8
[9] W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl., 322(1) (2006), 437-452.
9
[10] N.E. Wegge Olsen, K-Theory and $C^*$-Algebras, A Friendly Approch, Oxford University Press, Oxford, England, 1993.
10
ORIGINAL_ARTICLE
Some results on the block numerical range
The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.
https://wala.vru.ac.ir/article_25012_c4ff34a31d45ccb5ef9f7bc71791f5b0.pdf
2017-08-01
43
51
10.22072/wala.2017.51809.1088
block numerical range
nonnegative matrix
numerical range
Perron-Frobenius theory
Mostafa
Zangiabadi
zangiabadi1@gmail.com
1
University of Hormozgan
LEAD_AUTHOR
Hamid Reza
Afshin
afshin@vru.ac.ir
2
Vali-e-Asr University of Rafsanjan
AUTHOR
[1] K.H. Forster and N. Hartanto, On the block numerical range of nonnegative matrices, Oper. Theory: Adv. Appl., 188 (2008), 113-133.
1
[2] K.E. Gustafson and D.K.M. Rao, Numerical range: The field of values of linear operators and matrices, Springer-Verlag, New York, 1997.
2
[3] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
3
[4] R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
4
[5] J.N. Issos, The Field of Values of Non-Negative Irreducible Matrices, Ph.D. Thesis, Auburn University, 1966.
5
[6]H. Langer and C. Tretter, Spectral decomposition of some nonselfadjoint block operator matrices, J. Oper. Theory, 39(2) (1998), 339-359.
6
[7] C.K. Li, B.S. Tam and P.Y. Wu, The numerical range of a nonnegative matrix, Linear Algebra Appl., 350 (2002), 1-23.
7
[8] J. Maroulas, P.J. Psarrakos and M.J. Tsatsomeros, Perron-Frobenius type results on the numerical range, Linear Algebra Appl., 348 (2002), 49--62.
8
[9] H. Mink, Nonnegative Matrices, Wiley, New York, 1988.
9
[10] A. Salemi, Total decomposition and the block numerical range, Banach J. Math. Anal., 5(1) (2011), 51-55.
10
[11] C. Tretter and M. Wagenhofer, The block numerical range of an $ n\times n $ block operator matrix, SIAM J. Matrix Anal. Appl., 24(4) (2003), 1003--1017.
11
ORIGINAL_ARTICLE
Wavelet-based numerical method for solving fractional integro-differential equation with a weakly singular kernel
This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel. First, a collocation method based on Haar wavelets (HW), Legendre wavelet (LW), Chebyshev wavelets (CHW), second kind Chebyshev wavelets (SKCHW), Cos and Sin wavelets (CASW) and BPFs are presented for driving approximate solution FIDEs with a weakly singular kernel. Error estimates of all proposed numerical methods are given to test the convergence and accuracy of the method. A comparative study of accuracy and computational time for the presented techniques is given.
https://wala.vru.ac.ir/article_29387_eba4b5ca1c590ac187007f13d8603195.pdf
2017-08-01
53
73
10.22072/wala.2017.52567.1091
Fractional integro-differential equation
Weakly singular integral kernel
Collocation method, Error estimates
Fakhrodin
Mohammadi
f.mohammadi62@hotmail.com
1
Department of Mathematics‎, ‎University of ‎Hormozgan‎, ‎P‎. ‎O‎. ‎Box 3995‎, ‎Bandarabbas‎, ‎Iran
LEAD_AUTHOR
Armando
Ciancio
aciancio@unime.it
2
Department of Biomedical Sciences and Morphological and Functional Imaging‎,‎ University of Messina‎, ‎via Consolare Valeria 1‎, ‎98125 MESSINA‎, ‎Italy
AUTHOR
[1] S. Arbabi, A. Nazari and M.T. Darvishi, A two-dimensional Haar wavelets method for solving systems of PDEs. Appl. Math. Comput., 292 (2017), 33-46.
1
[2] C. Cattani, Local Fractional Calculus on Shannon Wavelet Basis, Nonlinear Physical Science, 2015.
2
[3] C. Cattani, Shannon wavelets for the solution of integro-differential equations, Math. Probl. Eng., 2010 (2010), doi:10.1155/2010/408418.
3
[4] C. Cattani, Shannon wavelets theory, Math. Probl. Eng., 2008 (2008), doi:10.1155/2008/164808.
4
[5] C. Cattani and A. Kudreyko, Harmonic wavelet method towards solution of the Fredholm type integral equations of the second kind, Appl. Math. Comput., 215(12) (2010), 4164-4171.
5
[6] I. Celik, Chebyshev Wavelet collocation method for solving generalized Burgers–Huxley equation, Math. Methods Appl. Sci., 39(3) (2016), 366--377.
6
[7] C.K. Chui, An Introduction to Wavelets, (Wavelet Analysis and Its Applications), vol. 1, Elsevier Press, Amsterdam 1992.
7
[8] E. Hernandez and G. Weiss, A First Course on Wavelets, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1996.
8
[9] M.H. Heydari, M.R. Hooshmandasl, F.M. Ghaini and C. Cattani, Wavelets method for solving fractional optimal control problems, Appl. Math. Comput., 286} (2016) 139-154.
9
[10] M.H. Heydari, M.R. Hooshmandasl and F. Mohammadi, Two-Dimensional Legendre Wavelets for Solving Time-Fractional Telegraph Equation, Adv. Appl. Math. Mech., 6(2) (2014), 247-260.
10
[11] M.R. Hooshmandasl, M.H. Heydari and C. Cattani, Numerical solution of fractional sub-diffusion and time-fractional diffusion-wave equations via fractional-order Legendre functions, Eur. Phys. J. Plus, (2016) 131-268, doi:10.1140/epjp/i2016-16268-2.
11
[12] A. Kilicman and Z.A. Zhour, Kronecker operational matrices for fractional calculus and some applications, Appl. Math. Comput., 187(1) (2007), 250-65.
12
[13] Y. Li, Solving a nonlinear fractional differential equation using Chebyshev wavelets, Commun. Nonlinear Sci. Numer. Simul., 15 (2010), 2284--2292.
13
[14] F. Mohammadi, A Chebyshev wavelet operational method for solving stochastic Volterra-Fredholm integral equations, Int. J. Appl. Math. Res., 4(2) (2015), 217-227.
14
[15] F. Mohammadi, A wavelet-based computational method for solving stochastic Ito-Volterra integral equations, J. Comput. Phys., 298 (2015), 254-265.
15
[16] F. Mohammadi, Numerical solution of Bagley-Torvik equation using Chebyshev wavelet operational matrix of fractional derivative, Int. J. Adv. Appl. Math. Mech., 2(1) (2014), 83-91.
16
[17] F. Mohammadi, Numerical solution of stochastic Ito-Volterra integral equations using Haar wavelets, Numer. Math., Theory Methods Appl., 9(3) (2016), 416-431.
17
[18] F. Mohammadi and M.M. Hosseini, A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations, J. Franklin Inst., 348(8) (2011), 1787-1796.
18
[19] F. Mohammadi and M.M. Hosseini, Legendre wavelet method for solving linear stiff systems, Journal of Advanced Research in Differential Equations, 2(1) (2010), 47-57.
19
[20] S.T. Mohyud-Din, A. Ali and B. Bin-Mohsin, On biological population model of fractional order, Int. J. Biomath., 9 (2016), doi:10.1142/S1793524516500704.
20
[21] S.T. Mohyud-Din, A. Waheed and M.M. Rashidi, A study of nonlinear age-structured population models, Int. J. Biomath., 9 (2016), doi:10.1142/S1793524516500911.
21
[22] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
22
[23] P. Rahimkhani, Y. Ordokhani, and E. Babolian, A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations, Numer. Algorithms, 74(1) (2017), 223-245.
23
[24] S.S. Ray and A.K. Gupta, Numerical solution of fractional partial differential equation of parabolic type with Dirichlet boundary conditions using Two-dimensional Legendre wavelets method, Journal of Computational and Nonlinear Dynamics, 11(1) (2016), doi:10.1115/1.4028984.
24
[25] H. Saeedi, Application of the haar wavelets in solving nonlinear fractional Fredholm intergro-differential equations, J. Mahani Math. Res. Cent., 2(1) (2012), 15-28.
25
[26] H. Saeedi and M. Mohseni Moghadam, Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets, Commun. Nonlinear Sci. Numer. Simul., 16(3) (2011), 1216-1226.
26
[27] H. Saeedi, M. Mohseni Moghadam, M. Mollahasani and G.N. Chuev, A CAS wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order, Commun. Nonlinear. Sci. Numer. Simul., 16(3) (2011), 1154-63.
27
[28] S.C. Shiralashetti and A. B. Deshi, An efficient Haar wavelet collocation method for the numerical solution of multi-term fractional differential equations, Nonlinear Dyn., 83(2) (2016), 293-303.
28
[29] Y. Wang and Q. Fan, The second kind Chebyshev wavelet method for solving fractional differential equations, Appl. Math. Comput., 218(17) (2012), 8592-8601.
29
[30] Y. Wang and L. Zhu, SCW method for solving the fractional integro-differential equations with a weakly singular kernel, Appl. Math. Comput., 275 (2016), 72-80.
30
[31] X.J. Yang, J.T. Machado, D. Baleanu and C. Cattani, On exact traveling-wave solutions for local fractional Korteweg-de Vries equation, Chaos, 26(8) (2016), doi: 10.1063/1.4960543.
31
[32] X.J. Yang, J.T. Machado and J. Hristov, Nonlinear dynamics for local fractional Burgers equation arising in fractal flow, Nonlinear Dyn., 84(1) (2016), 3-7.
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[33] X.J. Yang, J.T. Machado and H.M. Srivastava, A new numerical technique for solving the local fractional diffusion equation: two-dimensional extended differential transform approach, Appl. Math. Comput., 274 (2016), 143-151.
33
[34] X.J. Yang, H.M. Srivastava and C. Cattani, Local fractional homotopy perturbation method for solving fractal partial differential equations arising in mathematical physics, Rom. Rep. Phys., 67(3) (2015), 752-761.
34