# A class of Fredholm equations and systems of equations related to the Kontorovich-Lebedev and the Fourier integral transforms

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### "A class of Fredholm equations and s..." refers background in this paper

...1) with Γ = [0, T ] and the kernel is a periodic function that has been studied by many authors (see [1] and references therein)....

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### "A class of Fredholm equations and s..." refers background or methods in this paper

...Proof In order to prove this theorem, we use the generalized convolution for the Kontorovich–Lebedev, Fourier sine transforms which is defined by (see [17]):...

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...Namely, we use the convolutions and generalized convolutions related to the Kontorovich–Lebedev (K ), Fourier sine (Fs ), Fourier cosine (Fc ) transforms (see [12, 16, 17]) and their inverses....

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...1), we will use the generalized convolution with the weight function γ1(y) for the Kontorovich–Lebedev and the Fourier sine transform ( f γ1 ∗ 1 h ) (see [17]) defined by (3....

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...These convolutions, generalized convolution were studied in [6, 15, 17]....

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...Proof First, we recall the generalized convolution for the Kontorovich–Lebedev, Fourier cosine (see [17]), defined by (f γ1 ∗ 3 h)(x) := 1 2π ∫ R+2 1 x [e−x cosh(τ+θ) + e−x cosh(τ−θ)]f(τ)h(θ)dτdθ, x > 0, (3....

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### "A class of Fredholm equations and s..." refers background or methods in this paper

...[17] Yakubovich SB, Britvina LE....

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...[16] Yakubovich SB, Britvina LE....

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...Namely, we use the convolutions and generalized convolutions related to the Kontorovich–Lebedev (K ), Fourier sine (Fs ), Fourier cosine (Fc ) transforms (see [12, 16, 17]) and their inverses....

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...The function space Lα,βp is introduced in a research of Yakubovich and Britvina [16] Lα,βp ≡ Lp(R+,K0(βx)xα), α ∈ R, 0 β ≤ 1....

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...11) The generalized convolution for the Kontorovich–Lebedev, Fourier cosine transforms (see [16]) is defined by...

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