# Semyon Yakubovich

2018
Identities involving Bernoulli and Euler polynomials. Integral Transforms and Special Functions. . 2018;29(1):43-61.
On the curious series related to the elliptic integrals. The Ramanujan Journal. 2018;45(3):797-815.
On the Weber integral equation and solution to the Weber–Titchmarsh problem. Journal of Mathematical Analysis and Applications. 2018;460(1):400-410.
The spectral expansion approach to index transforms and connections with the theory of diffusion processes. Commun. Pure Appl. Anal.. 2018;17:2351-2378.
Index transforms with Weber-type kernels . Integral Transforms and Special Functions. 2018;29(3):171-188.
2017
On the generalized Dixon integral equation. Intern. Journ. of Math. And Comput.. 2017;28(1):25-32.
New classes of non-convolution integral equations arising from Lie symmetry analysis of hyperbolic PDEs. J. Differential Equations. 2017;263(11):7412-7447.
Lebedev type índex transforms with the squares of the associated Legendre functions. Acta Math., Hungar. . 2017;153(1):57-74.
2016
Index transforms with the squares of Bessel functions. Integral Transforms Spec. Funct.. 2016;27(12):981-994.
Closed-form evaluation of two-dimensional static lattice sums. Proc. R. Soc. A. 2016;472: 20160510.
New index transforms of the Lebedev–Skalskaya type. Integral Transforms and Special Functions. 2016;27(2):137-152.
On some properties of the Abel-Goncharov polynomials and the Casas-Alvero problem. Integral Transforms and Special Functions. 2016;27(8):599-610.
Lebedev's type index transforms with the modified Bessel functions. Commun. Math. Anal.. 2016;19(2):68-81.
2015
On the generalized Lebedev index transform. J. Math. Anal. Appl.. 2015;429(1):184-203.
New summation and transformation formulas of the Poisson, Müntz, Möbius and Voronoi type. Integral Transforms Spec. Functions. 2015;26(10):768-795.
New index transforms with the product of Bessel functions. Integral Transforms and Spec. Functions. 2015;26(12):939-955.
Certain identities, connection and explicit formulas for the Bernoulli and Euler numbers and the Riemann zeta-values. Analysis (Berlin). 2015;35:59-71.
2014
Time-dependent problems for a wedge via Kontorovich-Lebedev's transform. Bull. Malays. Math. Sci. Soc. (2). 2014;37:671-680.
The Plancherel, Titchmarsh and convolution theorems for the half-Hartley transform. Integral Transforms Spec. Funct.. 2014;25:836-848.
On the iterated Stieltjes transform and its convolution with applications to singular integral equations. Integral Transforms Spec. Funct.. 2014;25:398-411.
Integral and series transformations via Ramanujan's identities and Salem's type equivalences to the Riemann hypothesis. Integral Transforms Spec. Funct.. 2014;25:255-271.
On a polynomial sequence associated with the Bessel operator. Proc. Amer. Math. Soc.. 2014;142:467-482.
Polynomial problems of the Casas-Alvero type. J. Class. Anal. . 2014;4(2):97-120.
On special cases of Boas-Buck-type polynomial sequences.. 2014;Analytic number theory, approximation theory, and special functions:705-720.
On the half-Hartley transform, its iteration and compositions with Fourier transforms. J. Integral Equations Appl. . 2014;26(4):581-608.
Extremely Abundant Numbers and the Riemann Hypothesis. Journal of Integer Sequences. 2014;17(2):Article 14.2.8.
New inversion, convolution and Titchmarsh's theorems for the half-Hilbert transform. Integral Transforms Spec. Funct.. 2014;25:955-968.
2013
A class of index transforms generated by the Mellin and Laplace operators. J. Math. Anal. Appl.. 2013;403:333-343.
Central factorials under the Kontorovich-Lebedev transform of polynomials. Integral Transforms Spec. Funct.. 2013;24:217-238.
A Voronoi-type summation formula involving $\sigma_{\rm i\tau(n)$ and index transforms. Integral Transforms Spec. Funct.. 2013;24:98-110.
The use of the Kontorovich-Lebedev transform in an analysis of regularized Schrödinger equation. Integral Transforms Spec. Funct.. 2013;24:9-22.
A convolution operator related to the generalized Mehler-Fock and Kontorovich-Lebedev transforms. Results Math.. 2013;63:511-528.
On the Yor integral and a system of polynomials related to the Kontorovich-Lebedev transform. Integral Transforms Spec. Funct.. 2013;24:672-683.
On a heat kernel for the index Whittaker transform. Carpathian J. Math.. 2013;29:231-238.
Another proof of Spira's inequality and its application to the Riemann hypothesis. Journal of Mathematical Inequalities. 2013;7(2):167-174.
The Kontorovich-Lebedev transform as a map between $d$-orthogonal polynomials. Stud. Appl. Math.. 2013;131:229-265.
Another proof of Spira's inequality and its application to the Riemann hypothesis. J. Math. Inequal.. 2013;7:167-174.
On some Rajchman measures and equivalent Salem's problem. Commun. Math. Anal.. 2013;14:28-41.
2012
A new Kontorovich-Lebedev-like transformation. Commun. Math. Anal.. 2012;13:86-99.
Fundamental solutions of the fractional two-parameter telegraph equation. Integral Transforms Spec. Funct.. 2012;23:509-519.
An index integral and convolution operator related to the Kontorovich-Lebedev and Mehler-Fock transforms. Complex Anal. Oper. Theory. 2012;6:947-970.
Voronoi-Nasim summation formulas and index transforms. Integral Transforms Spec. Funct.. 2012;23:369-388.
On a Riemann-Liouville fractional analog of the Laplace operator with positive energy. Integral Transforms Spec. Funct.. 2012;23:277-295.
Corrigendum to the note The Fourier-Stieltjes transform of Minkowski's $?(x)$ function and an affirmative answer to Salem's problem'' [C. R. Acad. Sci. Paris, Ser. I 349 (11–12) (2011) 633–636] [\refcno 2817381]. C. R. Math. Acad. Sci. Paris. 2012;350:147.
2011
The heat kernel and Heisenberg inequalities related to the Kontorovich-Lebedev transform. Commun. Pure Appl. Anal.. 2011;10:745-760.
Multidimensional Kontorovich-Lebedev transforms. Integral Transforms Spec. Funct.. 2011;22:123-141.
A radial version of the Kontorovich-Lebedev transform in the unit ball. Opuscula Math.. 2011;31:137-146.
A general class of Voronoi's and Koshliakov-Ramanujan's summation formulas involving $d_k(n)$. Integral Transforms Spec. Funct.. 2011;22:801-821.
Index integral representations for connection between Cartesian, cylindrical, and spheroidal systems. Integral Transforms Spec. Funct.. 2011;22:549-560.
The Fourier-Stieltjes transform of Minkowski's $?(x)$ function and an affirmative answer to Salem's problem. C. R. Math. Acad. Sci. Paris. 2011;349:633-636.
2010
Properties of index transforms in modeling of nanostructures and plasmonic systems. J. Math. Phys.. 2010;51:023518, 30.
On the Watson $L_2$-theory for index transforms II. Integral Transforms Spec. Funct.. 2010;21:663-673.
An analog of Morgan's theorem for the Kontorovich-Lebedev transform. Adv. Pure Appl. Math.. 2010;1:159-162.
Generalized Fourier transform associated with the differential operator $D_z^n$ in the complex domain. Integral Transforms Spec. Funct.. 2010;21:541-555.
On the Watson $L_2$-theory for index transforms I. Integral Transforms Spec. Funct.. 2010;21:381-397.
Donoho-Stark and Paley-Wiener theorems for the $G$-transform. Adv. in Appl. Math.. 2010;45:108-124.
Convolutions related to the Fourier and Kontorovich-Lebedev transforms revisited. Integral Transforms Spec. Funct.. 2010;21:259-276.
A class of integral equations and index transformations related to the modified and incomplete Bessel functions. J. Integral Equations Appl.. 2010;22:141-164.
Eigenfunctions and fundamental solutions of the fractional two-parameter Laplacian. Int. J. Math. Math. Sci.. 2010:Art. ID 541934, 18.
2009
A double index transform with a product of Macdonald's functions revisited. Opuscula Math.. 2009;29:313-329.
On the orthogonality of the MacDonald's functions. J. Math. Anal. Appl.. 2009;360:380-390.
Convolution operators related to the Fourier cosine and Kontorovich-Lebedev transformations. Results Math.. 2009;55:175-197.
A class of polynomials and discrete transformations associated with the Kontorovich-Lebedev operators. Integral Transforms Spec. Funct.. 2009;20:551-567.
Harmonic analysis of the Lebedev-Stieltjes integrals. Asian-Eur. J. Math.. 2009;2:307-320.
On the theory of convolution integral equations related to Lebedev's type operators. Sarajevo J. Math.. 2009;5(17):119-132.
Beurling's theorems and inversion formulas for certain index transforms. Opuscula Math.. 2009;29:93-110.
2008
Asymptotic and summation formulas related to the Lebedev integrals. Integral Transforms Spec. Funct.. 2008;19:293-304.
Hardy-type theorem for orthogonal functions with respect to their zeros. The Jacobi weight case. J. Math. Anal. Appl.. 2008;341:803-812.
$L_2$-interpretation of the Kontorovich-Lebedev integrals. Int. J. Pure Appl. Math.. 2008;42:99-110.
On a progress in the Kontorovich-Lebedev transform theory and related integral operators. Integral Transforms Spec. Funct.. 2008;19:509-534.
Uncertainty principles for the Kontorovich-Lebedev transform. Math. Model. Anal.. 2008;13:289-302.
2007
A convolution related to the inverse Kontorovich-Lebedev transform. Sarajevo J. Math.. 2007;3(16):215-232.
2006
Certain isometries related to the bilateral Laplace transform. Math. Model. Anal.. 2006;11:331-346.
On a testing-function space for distributions associated with the Kontorovich-Lebedev transform. Collect. Math.. 2006;57:279-293.
The Plancherel and Hausdorff-Young type theorems for an index transformation. Z. Anal. Anwend.. 2006;25:193-204.
On the Plancherel theorem for the Olevskii transform. Acta Math. Vietnam.. 2006;31:249-260.
$L_2$-boundedness of the gamma-product transform. Liet. Mat. Rink.. 2006;46:285-297.
A distribution associated with the Kontorovich-Lebedev transform. Opuscula Math.. 2006;26:161-172.
2005
A real inversion formula for the bilateral Laplace transform. Izv. Nats. Akad. Nauk Armenii Mat.. 2005;40:67-79.
The Kontorovich-Lebedev transformation on Sobolev type spaces. Sarajevo J. Math.. 2005;1(14):211-234.
$L_P$-boundedness of general index transforms. Liet. Mat. Rink.. 2005;45:127-147.
Analog of the Hausdorff-Young theorem for the Lebedev integral. Integral Transforms Spec. Funct.. 2005;16:597-607.
2004
Index transforms associated with generalized hypergeometric functions. Math. Methods Appl. Sci.. 2004;27:35-46.
On the Lebedev transformation in Hardy's spaces. Int. J. Math. Math. Sci.. 2004:3603-3616.
On a new index transformation related to the product of Macdonald functions. Rad. Mat.. 2004;13:63-85.
On the least values of $L_p$-norms for the Kontorovich-Lebedev transform and its convolution. J. Approx. Theory. 2004;131:231-242.
2003
Convolution Hilbert spaces associated with the Kontorovich-Lebedev transformation. Thai J. Math.. 2003;1:9-16.
Boundedness and inversion properties of certain convolution transforms. J. Korean Math. Soc.. 2003;40:999-1014.
On the Kontorovich-Lebedev transformation. J. Integral Equations Appl.. 2003;15:95-112.
Integral transformations by the index of Lommel's function. Period. Math. Hungar.. 2003;46:223-233.
On the integral transformation associated with the product of gamma-functions. Port. Math. (N.S.). 2003;60:337-351.
Integral transforms of the Kontorovich-Lebedev convolution type. Collect. Math.. 2003;54:99-110.
2002
Convolutions and neutrix convolution in connection with the incomplete gamma function. Rad. Mat.. 2002;11:37-47.
Index transforms associated with products of Whittaker's functions. J. Comput. Appl. Math.. 2002;148:419-427.
Index transforms associated with Bessel and Lommel functions. Z. Anal. Anwendungen. 2002;21:627-638.
On the index integral transformation with Nicholson's function as the kernel. J. Math. Anal. Appl.. 2002;269:689-701.
2001
Results on the sine integral and the neutrix convolution. Rad. Mat.. 2001;10:171-180.
2000
Multiple orthogonal polynomials associated with Macdonald functions. Integral Transform. Spec. Funct.. 2000;9:229-244.
The Cherry transform and its relationship with a singular Sturm-Liouville problem. Q. J. Math.. 2000;51:371-383.
Integral transformation associated with the Macdonald type kernels. East-West J. Math.. 2000;2:73-84.