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Abstract
In this paper for k ≥2, we introduce the idea of kth-order (Slant Toeplitz + Slant Hankel ) operators on the polydisk and discuss the commutativity, partial isometry and co-isometry properties. Further, we extend our study to the spectral properties.
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References
- Chandola, A., Pandey, R. M. , Agarwal, R., Rathour, L., and Mishra, V. N., On some properties and applications of the generalized m-parameter Mittag-Leffler function, Advanced Mathematical Models & Applications, 7 (2002), 130-145.
- Koca-Eskisehirli, B. B., Spectral Properties of Two Classes of Toeplitz Operators on Hp, 1 < p < ∞, Bull. Iran. Math. Soc., 48 (2022), 3047-3057.
- Mancera, C. H. and Paul, P. J., Properties of generalised Toeplitz operators, Integral equns. operator Theo., 40 (2001), 106-126.
- Farenick, D., The operator system of Toeplitz matrices, Trans. Amer. Math. Soc. Ser. B, 8 (2021), 999-1023.
- Basor, E. L. and Ehrhardt, T., On a Class of Toeplitz + Hankel operators, J. Reine Angew. Math., 213 (1999), 89-102.
- Datt, G. and Gupta, B., Analogue of slant Hankel operators on the Lebesgue space of n-torus”, Adv. Oper. Theory, 6 (2021), 66.
- Farid, G., Mehmood, S., Rathour, L., Mishra, L. N., Mishra, V. N., Fractional Hadamard and Fej´er-Hadamard inequalities associated with exp. (α, h − m)-convexity, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 30 (2023), 353-367.
- Rathour, L., Rehman, A. U., Bibi, S., Farid, G., and Mishra, L. N., k-fractional integral inequalities of Hadamard type for strongly exponentially (α, h−m)-convex functions, Applied Mathematics E-Notes, 23 (2023), 393-411.
- Hazarika, M. and Marik, S., Toeplitz and slant Toeplitz operators on the polydisk, Arab Journal of Mathematical Sciences, 27 (2021), 73-93.
- Sharma, M. K., Sadhna, Bhargava, A. K., Kumar, S., Rathour, L., Mishra, L. N., and Pandey, S., A Fermatean fuzzy ranking function in optimization of Intuitionistic fuzzy transportation problems, Advanced Mathematical Models & Applications, 7 (2022), 191-204.
- Sharma, M. K., Dhiman, N., Kumar, S., Rathour, L., and Mishra, V. N., Neutrosophic Monte Carlo Simulation Approach for Decision Making In Medical Diagnostic Process Under Uncertain Environment, International Journal of Neutrosophic Science, 22 (2023), 8-16.
- Hogeme, M. S., Woldaregay, M. M., Rathour, L., and Mishra, V. N., A stable numerical method for singularly perturbed Fredholm integro differential equation using exponentially fitted difference method, J. Comput. Appl. Math., 441 (2024), 115709.
- Toeplitz, O., Zur theoric der quadratischen and bilinearen formen von unendlichielen veranderlichen, Math. Anal., 70 (1911), 135.
- Fuhrman, P. A., On sums of Hankel operators, Proc. Amer. Math. Soc., 46 (1950), 65-68.
- Aiena P. and Triolo, S., Some Remarks on the Spectral Properties of Toeplitz Operators, Mediterr. J. Math, 16 (2019), 157-166.
- Hatman, P. and Winter, A., The Spectra of Toeplitz’s Matrices, Amer. J. Math., 72 (1954), 359-366.
- Negero, N.T., Duressa, G. F., Rathour, L., and Mishra, V.N., A novel fitted numerical scheme for singularly perturbed delay parabolic problems with two small parameters, Partial Differential Equations in Applied Mathematics, 8 (2023), 1-8.
- Arora, S. C., Batra, R., and Singh, M. P., Slant Hankel operators, Arch. Math., 42 (2006), 125-133.
- Didenko, V. D., and Silbermann, B., Some results on the invertibility of Toeplitz plus Hankel operators, Ann. Acad. Sci. Fenn. Math., 39 (2014), 443-461.
- Didenko, V. D. and Silbermann (2017), Invertibility and inverses of Toeplitz plus Hankel operators, Operator Theory, 72, 293-307.
- Lu, Y., Liu, C., and Yang, J., Commutativity of kth order slant Toeplitz operators, Math. Nachr., 9 (2010), 1304-1313.
References
Chandola, A., Pandey, R. M. , Agarwal, R., Rathour, L., and Mishra, V. N., On some properties and applications of the generalized m-parameter Mittag-Leffler function, Advanced Mathematical Models & Applications, 7 (2002), 130-145.
Koca-Eskisehirli, B. B., Spectral Properties of Two Classes of Toeplitz Operators on Hp, 1 < p < ∞, Bull. Iran. Math. Soc., 48 (2022), 3047-3057.
Mancera, C. H. and Paul, P. J., Properties of generalised Toeplitz operators, Integral equns. operator Theo., 40 (2001), 106-126.
Farenick, D., The operator system of Toeplitz matrices, Trans. Amer. Math. Soc. Ser. B, 8 (2021), 999-1023.
Basor, E. L. and Ehrhardt, T., On a Class of Toeplitz + Hankel operators, J. Reine Angew. Math., 213 (1999), 89-102.
Datt, G. and Gupta, B., Analogue of slant Hankel operators on the Lebesgue space of n-torus”, Adv. Oper. Theory, 6 (2021), 66.
Farid, G., Mehmood, S., Rathour, L., Mishra, L. N., Mishra, V. N., Fractional Hadamard and Fej´er-Hadamard inequalities associated with exp. (α, h − m)-convexity, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 30 (2023), 353-367.
Rathour, L., Rehman, A. U., Bibi, S., Farid, G., and Mishra, L. N., k-fractional integral inequalities of Hadamard type for strongly exponentially (α, h−m)-convex functions, Applied Mathematics E-Notes, 23 (2023), 393-411.
Hazarika, M. and Marik, S., Toeplitz and slant Toeplitz operators on the polydisk, Arab Journal of Mathematical Sciences, 27 (2021), 73-93.
Sharma, M. K., Sadhna, Bhargava, A. K., Kumar, S., Rathour, L., Mishra, L. N., and Pandey, S., A Fermatean fuzzy ranking function in optimization of Intuitionistic fuzzy transportation problems, Advanced Mathematical Models & Applications, 7 (2022), 191-204.
Sharma, M. K., Dhiman, N., Kumar, S., Rathour, L., and Mishra, V. N., Neutrosophic Monte Carlo Simulation Approach for Decision Making In Medical Diagnostic Process Under Uncertain Environment, International Journal of Neutrosophic Science, 22 (2023), 8-16.
Hogeme, M. S., Woldaregay, M. M., Rathour, L., and Mishra, V. N., A stable numerical method for singularly perturbed Fredholm integro differential equation using exponentially fitted difference method, J. Comput. Appl. Math., 441 (2024), 115709.
Toeplitz, O., Zur theoric der quadratischen and bilinearen formen von unendlichielen veranderlichen, Math. Anal., 70 (1911), 135.
Fuhrman, P. A., On sums of Hankel operators, Proc. Amer. Math. Soc., 46 (1950), 65-68.
Aiena P. and Triolo, S., Some Remarks on the Spectral Properties of Toeplitz Operators, Mediterr. J. Math, 16 (2019), 157-166.
Hatman, P. and Winter, A., The Spectra of Toeplitz’s Matrices, Amer. J. Math., 72 (1954), 359-366.
Negero, N.T., Duressa, G. F., Rathour, L., and Mishra, V.N., A novel fitted numerical scheme for singularly perturbed delay parabolic problems with two small parameters, Partial Differential Equations in Applied Mathematics, 8 (2023), 1-8.
Arora, S. C., Batra, R., and Singh, M. P., Slant Hankel operators, Arch. Math., 42 (2006), 125-133.
Didenko, V. D., and Silbermann, B., Some results on the invertibility of Toeplitz plus Hankel operators, Ann. Acad. Sci. Fenn. Math., 39 (2014), 443-461.
Didenko, V. D. and Silbermann (2017), Invertibility and inverses of Toeplitz plus Hankel operators, Operator Theory, 72, 293-307.
Lu, Y., Liu, C., and Yang, J., Commutativity of kth order slant Toeplitz operators, Math. Nachr., 9 (2010), 1304-1313.