The Cauchy problem for evolution equations with the Bessel operator of infinite order. I (Q1956624)
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scientific article; zbMATH DE number 5790451
| Language | Label | Description | Also known as |
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| English | The Cauchy problem for evolution equations with the Bessel operator of infinite order. I |
scientific article; zbMATH DE number 5790451 |
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The Cauchy problem for evolution equations with the Bessel operator of infinite order. I (English)
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23 September 2010
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Singular evolution equations of infinite order represent natural generalization of singular parabolic equations and contain the Bessel operator of infinite order with \(\varphi (B_\nu)=\sum_{k=0}^\infty c_k B^k_\nu\) instead of the relevant finite sum. Here \(B_\nu\) is the Bessel operator of order \(\nu> -1/2\). The paper contains necessary and sufficient conditions under which the Bessel operator of infinite order is bounded in certain spaces. The relevant convolution operators are studied.
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Bessel transformation
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distributions
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Bessel operator of infinite order
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convolutors
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multiplicators
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