Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2024, Cilt: 2 Sayı: 1, 33 - 38, 25.06.2024
https://doi.org/10.26650/ijmath.2024.00013

Öz

Kaynakça

  • Albayrak D. and Dernek N., On some generalized integral transforms and Parseval-Goldstein type relations, Hacet. J. Math. Stat., 50(2):526-540, 2021. google scholar
  • Albayrak D., Some Parseval-Goldstein type theorems for generalized integral transforms, Math. Sci. Appl. E-Notes, 12(2):81-92, 2024, DOI: https://doi.org/10.36753/mathenot.1362335. google scholar
  • Dernek N., Srivastava H. M. and Yürekli O., Parseval-Goldstein type identities involving the L4-transform and the P4-transform and their applications, Integral Transforms Spec. Funct., 18:397-408, 2007. google scholar
  • Dernek N., Srivastava H. M. and Yürekli O., Some Parseval-Goldstein type identities involving the Fg,2-transform, the Fc,2-transform and the P4-transform and their applications, Appl. Math. Comput., 202:327-337, 2008. google scholar
  • Erdelyi A., Magnus W., Oberhettinger F. and Tricomi F. G., Higher transcendental functions, McGraw-Hill Book Company, Vol (1), New York, 1953. google scholar
  • Erdelyi A., Magnus W., Oberhettinger F. and Tricomi F. G., Higher transcendental functions, McGraw-Hill Book Company, Vol (2), New York, 1953. google scholar
  • Gonzalez B. J. and Negrın E. R., Abelian theorems for distributional Kontorovich-Lebedev and Mehler-Fock transforms of general order, Banach J. Math. Anal., 13(3):524-537, 2019. google scholar
  • Gonzalez B. J. and Negrın E. R., Lp -inequalities and Parseval-type relations for the Mehler-Fock transforms of general order, Ann. Funct. Anal., 8(2): 231-239, 2017. google scholar
  • Gonzalez B. J. and Negrın E. R., On Operators with Complex Gaussian Kernels over Lp Spaces, Filomat, 33(9):2861-2866, 2019. google scholar
  • Gonzalez B. J. and Negrın E. R., New Lp -inequalities for hyperbolic weights concerning the operators with complex Gaussian kernels, Banach J. Math. Anal., 12(2): 399-421, 2018. google scholar
  • Hayek N., Gonzalez B. J. and Negrın E. R., Abelian theorems for the index 2Fi-transform, Rev. Tecn. Fac. Ingr. Univ. Zulia 15(3), 167-171, 1992. google scholar
  • Hayek N. and Gonzalez B. J., A convolution theorem for the index 2F1-transform, J. Inst. Math. Comput. Sci. Math. Ser. 6(1), 21-24, 1993. google scholar
  • Hayek N. and Gonzalez B.J., On the distributional index 2F1-transform, Math. Nachr. 165, 15-24, 1994. google scholar
  • Hayek N. and Gonzalez B. J., A convolution theorem for the distributional index 2F1-transform, Rev. Roumaine Math. Pures Appl. 42(7-8), 567-578, 1997. google scholar
  • Karataş H. B., Kumar D. and Uçar F., Some iteration and Parseval-Goldstein type identities with their applications, Adv. Appl. Math. Sci., 29(2), 563-574, 2020. google scholar
  • Lebedev N. N., The Parseval theorem for the Mehler-Fock integral transform, Dokl. Akad. Nauk, 68(3):445-448, 1949.(in Russian). google scholar
  • Maan J. and Negrın E. R., Parseval-Goldstein type theorems for the Kontorovich-Lebedev transform and the Mehler-Fock transform of general order, Filomat, 2024 (accepted for publication). google scholar
  • Maan J. and Negrın E. R., Parseval-Goldstein type theorems for the index 2Fi -transform, Int. J. Appl. Comput. Math, 10(69), 2024, https://doi.org/10.1007/s40819-024-01713-9. google scholar
  • Maan J. and Negrın E. R., Parseval-Goldstein type theorems for the Lebedev-Skalskaya transforms, 2024 (submitted). google scholar
  • Maan J. and Prasad A., Wave packet transform and wavelet convolution product involving the index Whittaker transform, Ramanujan J., DOI: https://doi.org/10.1007/s11139-023-00793-3, 2024. google scholar
  • Maan J. and Prasad A., Weyl operator associated with index Whittaker transform, J. Pseudo-Differ. Oper. Appl., 13(3):1-12, 2022. google scholar
  • Maan J., Gonzalez B. J. and Negrın E. R., Abelian theorems for the index 2Fi -transform over distributions of compact support and generalized functions, Filomat, 37(30):10229-10236, 2023. google scholar
  • Mandal U. K. and Prasad A., Lebedev-Skalskaya transforms and allied operators on certain function spaces, Integral Transforms Spec. Funct., 33(4): 320-340, 2022. google scholar
  • Mandal U. K., Prasad A., Gupt A. K., Reverse convolution inequalities for Lebedev-Skalskaya transforms, Forum Math., DOI: 10.1515/forum-2021-0313, 2022. google scholar
  • Negrın E. R., Operators with complex Gaussian kernels: boundednessproperties, Proc. Am. Math. Soc., 123(4): 1185-1190, 1995. google scholar
  • Naylor D., On an asymptotic expansion ofthe Kontorovich-Lebedev transform, Appl. Anal., 39(4):249-263, 1990. google scholar
  • Prasad A. and Mandal U. K. The Kontorovich-Lebedev Transform and Sobolev Type Space, Complex Anal. Oper. Theory, 12:669-681, 2018. google scholar
  • Sousa R., Guerra M. and Yakubovich S., Levy processes with respect to the index Whittaker convolution, Trans Amer Math Soc., 374(4):2383-2419, 2020. google scholar
  • Sousa R., Guerra M. and Yakubovich S., On the product formula and convolution associated with the index Whittaker transform, J. Math. Anal. Appl., 475(1):939-965, 2019. google scholar
  • Srivastava H. M. and Yürekli O., A theorem on a Stieltjes-type integral transform and its applications, Complex Variables Theory Appl., 28(2):159-168, 1995. google scholar
  • SrivastavaH. M., Gonzalez B. J. and Negrın E. R., New Lp-boundednessproperties for the Kontorovich-Lebedev andMehler-Fock transforms, Integral Transforms Spec. Funct., 27(10):835-845, 2016. google scholar
  • Yakubovich S., An Index integral and convolution operator related to the Kontorovich-Lebedev and Mehler-Fock transforms, Complex Anal. Oper. Theory, 6(4):947-970, 2012. google scholar
  • Yürekli O., A Parseval-type Theorem Applied to Certain Integral Transforms, IMA J. Appl. Math., 42:241-249, 1989. google scholar
  • Yürekli O., A theorem on the generalized Stieltjes transform, J. Math. Anal. Appl., 168(1):63-71, 1992. google scholar

Parseval-Goldstein type theorems for integral transforms in a general setting

Yıl 2024, Cilt: 2 Sayı: 1, 33 - 38, 25.06.2024
https://doi.org/10.26650/ijmath.2024.00013

Öz

This research paper explores Parseval-Goldstein type relations concerning general integral operators. It investigates the continuity properties of these operators and their adjoints over Lebesgue spaces. Through rigorous analysis, the study elucidates the intricate connections between these operators and sheds light on their behaviour within functional spaces. By exploring the convergence and stability of these relations, the paper contributes to a deeper understanding of integral operators behaviour and their implications in various mathematical contexts. The paper also examines specific cases of the main index transforms, including the KontorovichLebedev transform, the Mehler-Fock transform of general order, the index 2𝐹1-transform, the Lebedev-Skalskaya transforms and the index Whittaker transform, as well as operators with complex Gaussian kernels, contributing valuable insights into their behaviour and applications.

Kaynakça

  • Albayrak D. and Dernek N., On some generalized integral transforms and Parseval-Goldstein type relations, Hacet. J. Math. Stat., 50(2):526-540, 2021. google scholar
  • Albayrak D., Some Parseval-Goldstein type theorems for generalized integral transforms, Math. Sci. Appl. E-Notes, 12(2):81-92, 2024, DOI: https://doi.org/10.36753/mathenot.1362335. google scholar
  • Dernek N., Srivastava H. M. and Yürekli O., Parseval-Goldstein type identities involving the L4-transform and the P4-transform and their applications, Integral Transforms Spec. Funct., 18:397-408, 2007. google scholar
  • Dernek N., Srivastava H. M. and Yürekli O., Some Parseval-Goldstein type identities involving the Fg,2-transform, the Fc,2-transform and the P4-transform and their applications, Appl. Math. Comput., 202:327-337, 2008. google scholar
  • Erdelyi A., Magnus W., Oberhettinger F. and Tricomi F. G., Higher transcendental functions, McGraw-Hill Book Company, Vol (1), New York, 1953. google scholar
  • Erdelyi A., Magnus W., Oberhettinger F. and Tricomi F. G., Higher transcendental functions, McGraw-Hill Book Company, Vol (2), New York, 1953. google scholar
  • Gonzalez B. J. and Negrın E. R., Abelian theorems for distributional Kontorovich-Lebedev and Mehler-Fock transforms of general order, Banach J. Math. Anal., 13(3):524-537, 2019. google scholar
  • Gonzalez B. J. and Negrın E. R., Lp -inequalities and Parseval-type relations for the Mehler-Fock transforms of general order, Ann. Funct. Anal., 8(2): 231-239, 2017. google scholar
  • Gonzalez B. J. and Negrın E. R., On Operators with Complex Gaussian Kernels over Lp Spaces, Filomat, 33(9):2861-2866, 2019. google scholar
  • Gonzalez B. J. and Negrın E. R., New Lp -inequalities for hyperbolic weights concerning the operators with complex Gaussian kernels, Banach J. Math. Anal., 12(2): 399-421, 2018. google scholar
  • Hayek N., Gonzalez B. J. and Negrın E. R., Abelian theorems for the index 2Fi-transform, Rev. Tecn. Fac. Ingr. Univ. Zulia 15(3), 167-171, 1992. google scholar
  • Hayek N. and Gonzalez B. J., A convolution theorem for the index 2F1-transform, J. Inst. Math. Comput. Sci. Math. Ser. 6(1), 21-24, 1993. google scholar
  • Hayek N. and Gonzalez B.J., On the distributional index 2F1-transform, Math. Nachr. 165, 15-24, 1994. google scholar
  • Hayek N. and Gonzalez B. J., A convolution theorem for the distributional index 2F1-transform, Rev. Roumaine Math. Pures Appl. 42(7-8), 567-578, 1997. google scholar
  • Karataş H. B., Kumar D. and Uçar F., Some iteration and Parseval-Goldstein type identities with their applications, Adv. Appl. Math. Sci., 29(2), 563-574, 2020. google scholar
  • Lebedev N. N., The Parseval theorem for the Mehler-Fock integral transform, Dokl. Akad. Nauk, 68(3):445-448, 1949.(in Russian). google scholar
  • Maan J. and Negrın E. R., Parseval-Goldstein type theorems for the Kontorovich-Lebedev transform and the Mehler-Fock transform of general order, Filomat, 2024 (accepted for publication). google scholar
  • Maan J. and Negrın E. R., Parseval-Goldstein type theorems for the index 2Fi -transform, Int. J. Appl. Comput. Math, 10(69), 2024, https://doi.org/10.1007/s40819-024-01713-9. google scholar
  • Maan J. and Negrın E. R., Parseval-Goldstein type theorems for the Lebedev-Skalskaya transforms, 2024 (submitted). google scholar
  • Maan J. and Prasad A., Wave packet transform and wavelet convolution product involving the index Whittaker transform, Ramanujan J., DOI: https://doi.org/10.1007/s11139-023-00793-3, 2024. google scholar
  • Maan J. and Prasad A., Weyl operator associated with index Whittaker transform, J. Pseudo-Differ. Oper. Appl., 13(3):1-12, 2022. google scholar
  • Maan J., Gonzalez B. J. and Negrın E. R., Abelian theorems for the index 2Fi -transform over distributions of compact support and generalized functions, Filomat, 37(30):10229-10236, 2023. google scholar
  • Mandal U. K. and Prasad A., Lebedev-Skalskaya transforms and allied operators on certain function spaces, Integral Transforms Spec. Funct., 33(4): 320-340, 2022. google scholar
  • Mandal U. K., Prasad A., Gupt A. K., Reverse convolution inequalities for Lebedev-Skalskaya transforms, Forum Math., DOI: 10.1515/forum-2021-0313, 2022. google scholar
  • Negrın E. R., Operators with complex Gaussian kernels: boundednessproperties, Proc. Am. Math. Soc., 123(4): 1185-1190, 1995. google scholar
  • Naylor D., On an asymptotic expansion ofthe Kontorovich-Lebedev transform, Appl. Anal., 39(4):249-263, 1990. google scholar
  • Prasad A. and Mandal U. K. The Kontorovich-Lebedev Transform and Sobolev Type Space, Complex Anal. Oper. Theory, 12:669-681, 2018. google scholar
  • Sousa R., Guerra M. and Yakubovich S., Levy processes with respect to the index Whittaker convolution, Trans Amer Math Soc., 374(4):2383-2419, 2020. google scholar
  • Sousa R., Guerra M. and Yakubovich S., On the product formula and convolution associated with the index Whittaker transform, J. Math. Anal. Appl., 475(1):939-965, 2019. google scholar
  • Srivastava H. M. and Yürekli O., A theorem on a Stieltjes-type integral transform and its applications, Complex Variables Theory Appl., 28(2):159-168, 1995. google scholar
  • SrivastavaH. M., Gonzalez B. J. and Negrın E. R., New Lp-boundednessproperties for the Kontorovich-Lebedev andMehler-Fock transforms, Integral Transforms Spec. Funct., 27(10):835-845, 2016. google scholar
  • Yakubovich S., An Index integral and convolution operator related to the Kontorovich-Lebedev and Mehler-Fock transforms, Complex Anal. Oper. Theory, 6(4):947-970, 2012. google scholar
  • Yürekli O., A Parseval-type Theorem Applied to Certain Integral Transforms, IMA J. Appl. Math., 42:241-249, 1989. google scholar
  • Yürekli O., A theorem on the generalized Stieltjes transform, J. Math. Anal. Appl., 168(1):63-71, 1992. google scholar
Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
Bölüm Araştırma Makalesi
Yazarlar

Jeetendrasingh Maan 0000-0001-6569-8540

Emilio Negrín 0000-0002-5506-5050

Yayımlanma Tarihi 25 Haziran 2024
Gönderilme Tarihi 14 Nisan 2024
Kabul Tarihi 7 Haziran 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 2 Sayı: 1

Kaynak Göster

APA Maan, J., & Negrín, E. (2024). Parseval-Goldstein type theorems for integral transforms in a general setting. Istanbul Journal of Mathematics, 2(1), 33-38. https://doi.org/10.26650/ijmath.2024.00013
AMA Maan J, Negrín E. Parseval-Goldstein type theorems for integral transforms in a general setting. Istanbul Journal of Mathematics. Haziran 2024;2(1):33-38. doi:10.26650/ijmath.2024.00013
Chicago Maan, Jeetendrasingh, ve Emilio Negrín. “Parseval-Goldstein Type Theorems for Integral Transforms in a General Setting”. Istanbul Journal of Mathematics 2, sy. 1 (Haziran 2024): 33-38. https://doi.org/10.26650/ijmath.2024.00013.
EndNote Maan J, Negrín E (01 Haziran 2024) Parseval-Goldstein type theorems for integral transforms in a general setting. Istanbul Journal of Mathematics 2 1 33–38.
IEEE J. Maan ve E. Negrín, “Parseval-Goldstein type theorems for integral transforms in a general setting”, Istanbul Journal of Mathematics, c. 2, sy. 1, ss. 33–38, 2024, doi: 10.26650/ijmath.2024.00013.
ISNAD Maan, Jeetendrasingh - Negrín, Emilio. “Parseval-Goldstein Type Theorems for Integral Transforms in a General Setting”. Istanbul Journal of Mathematics 2/1 (Haziran 2024), 33-38. https://doi.org/10.26650/ijmath.2024.00013.
JAMA Maan J, Negrín E. Parseval-Goldstein type theorems for integral transforms in a general setting. Istanbul Journal of Mathematics. 2024;2:33–38.
MLA Maan, Jeetendrasingh ve Emilio Negrín. “Parseval-Goldstein Type Theorems for Integral Transforms in a General Setting”. Istanbul Journal of Mathematics, c. 2, sy. 1, 2024, ss. 33-38, doi:10.26650/ijmath.2024.00013.
Vancouver Maan J, Negrín E. Parseval-Goldstein type theorems for integral transforms in a general setting. Istanbul Journal of Mathematics. 2024;2(1):33-8.