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The maximal number of interior peak solutions concentrating on hyperplanes for a singularly perturbed Neumann problem
The heat kernel and Heisenberg inequalities related to the Kontorovich-Lebedev transform
1. | Department of Mathematics, Faculty of Sciences, University of Porto, Campo Alegre st., 687, Porto, 4169-007, Portugal |
References:
[1] |
M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions," Dover, New York, 1972. |
[2] |
R. Ma, Heisenberg inequalities for Jacobi transforms, J. Math. Anal. Appl., 332 (2007), 155-163.
doi: doi:10.1016/j.jmaa.2006.09.044. |
[3] |
E. H. Lieb and M. Loss, "Analysis," Graduate Studies in Math., Vol. 14, American Math. Soc., Providence, Rhode Island, 2001. |
[4] |
C. Monthus and A. Comtet, On the flux distribution in a one dimensional disordered system, J. Phys. I France, 4 (1994), 635-653. |
[5] |
A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, "Integrals and Series, Vol. I: Elementary Functions," Gordon and Breach, New York and London, 1986. |
[6] |
A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, "Integrals and Series, Vol. II: Special Functions," Gordon and Breach, New York and London, 1986. |
[7] |
I. N. Sneddon, "The Use of Integral Transforms," McGraw-Hill, New York, 1972. |
[8] |
S. B. Yakubovich and Yu. F. Luchko, "The Hypergeometric Approach to Integral Transforms and Convolutions," (Kluwers Ser. Math. and Appl.: Vol. 287), Dordrecht, Boston, London, 1994. |
[9] |
S. B. Yakubovich, "Index Transforms," World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1996. |
[10] |
S. B. Yakubovich, On the Kontorovich-Lebedev transformation, J. of Integral Equations and Appl., 15 (2003), 95-112.
doi: doi:10.1216/jiea/1181074947. |
[11] |
S. B. Yakubovich, Integral transforms of the Kontorovich-Lebedev convolution type, Collect. Math., 54 (2003), 99-110. |
[12] |
S. B. Yakubovich, Boundedness and inversion properties of certain convolution transforms, J. Korean Math. Soc., 40 (2003), 999-1014.
doi: doi:10.4134/JKMS.2003.40.6.999. |
[13] |
S. B. Yakubovich, On the least values of $L_p$-norms for the Kontorovich-Lebedev transform and its convolution, J. of Approximation Theory, 131 (2004), 231-242.
doi: doi:10.1016/j.jat.2004.10.007. |
[14] |
S. B. Yakubovich, The Kontorovich-Lebedev transformation on Sobolev type spaces, Sarajevo J. of Mathematics, 1 (2005), 211-234. |
[15] |
S. B. Yakubovich, On a testing -function space for distributions associated with the Kontorovich-Lebedev transform, Collect. Math., 57 (2006), 279-293. |
[16] |
S. B. Yakubovich, Uncertainty principles for the Kontorovich-Lebedev transform, Math. Modelling and Analysis, 13 (2008), 289-302.
doi: doi:10.3846/1392-6292.2008.13.289-302. |
[17] |
S. B. Yakubovich, A class of polynomials and discrete transformations associated with the Kontorovich-Lebedev operators, Integral Transforms and Special Functions, 20 (2009), 551-567.
doi: doi:10.1080/10652460802648473. |
[18] |
S. B. Yakubovich and R. Daher, An analog of Morgan's theorem for the Kontorovich-Lebedev transform, Adv. Pure Apll. Math., 1:2 (2010), 159-162.
doi: doi:10.1515/APAM.2010.010. |
[19] |
A. H. Zemanian, The Kontorovich-Lebedev transformation on distributions of compact support and its inversion, Math. Proc. Cambridge Philos. Soc., 77 (1975), 139-143.
doi: doi:10.1017/S0305004100049471. |
show all references
References:
[1] |
M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions," Dover, New York, 1972. |
[2] |
R. Ma, Heisenberg inequalities for Jacobi transforms, J. Math. Anal. Appl., 332 (2007), 155-163.
doi: doi:10.1016/j.jmaa.2006.09.044. |
[3] |
E. H. Lieb and M. Loss, "Analysis," Graduate Studies in Math., Vol. 14, American Math. Soc., Providence, Rhode Island, 2001. |
[4] |
C. Monthus and A. Comtet, On the flux distribution in a one dimensional disordered system, J. Phys. I France, 4 (1994), 635-653. |
[5] |
A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, "Integrals and Series, Vol. I: Elementary Functions," Gordon and Breach, New York and London, 1986. |
[6] |
A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, "Integrals and Series, Vol. II: Special Functions," Gordon and Breach, New York and London, 1986. |
[7] |
I. N. Sneddon, "The Use of Integral Transforms," McGraw-Hill, New York, 1972. |
[8] |
S. B. Yakubovich and Yu. F. Luchko, "The Hypergeometric Approach to Integral Transforms and Convolutions," (Kluwers Ser. Math. and Appl.: Vol. 287), Dordrecht, Boston, London, 1994. |
[9] |
S. B. Yakubovich, "Index Transforms," World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1996. |
[10] |
S. B. Yakubovich, On the Kontorovich-Lebedev transformation, J. of Integral Equations and Appl., 15 (2003), 95-112.
doi: doi:10.1216/jiea/1181074947. |
[11] |
S. B. Yakubovich, Integral transforms of the Kontorovich-Lebedev convolution type, Collect. Math., 54 (2003), 99-110. |
[12] |
S. B. Yakubovich, Boundedness and inversion properties of certain convolution transforms, J. Korean Math. Soc., 40 (2003), 999-1014.
doi: doi:10.4134/JKMS.2003.40.6.999. |
[13] |
S. B. Yakubovich, On the least values of $L_p$-norms for the Kontorovich-Lebedev transform and its convolution, J. of Approximation Theory, 131 (2004), 231-242.
doi: doi:10.1016/j.jat.2004.10.007. |
[14] |
S. B. Yakubovich, The Kontorovich-Lebedev transformation on Sobolev type spaces, Sarajevo J. of Mathematics, 1 (2005), 211-234. |
[15] |
S. B. Yakubovich, On a testing -function space for distributions associated with the Kontorovich-Lebedev transform, Collect. Math., 57 (2006), 279-293. |
[16] |
S. B. Yakubovich, Uncertainty principles for the Kontorovich-Lebedev transform, Math. Modelling and Analysis, 13 (2008), 289-302.
doi: doi:10.3846/1392-6292.2008.13.289-302. |
[17] |
S. B. Yakubovich, A class of polynomials and discrete transformations associated with the Kontorovich-Lebedev operators, Integral Transforms and Special Functions, 20 (2009), 551-567.
doi: doi:10.1080/10652460802648473. |
[18] |
S. B. Yakubovich and R. Daher, An analog of Morgan's theorem for the Kontorovich-Lebedev transform, Adv. Pure Apll. Math., 1:2 (2010), 159-162.
doi: doi:10.1515/APAM.2010.010. |
[19] |
A. H. Zemanian, The Kontorovich-Lebedev transformation on distributions of compact support and its inversion, Math. Proc. Cambridge Philos. Soc., 77 (1975), 139-143.
doi: doi:10.1017/S0305004100049471. |
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