Convolutional Calculus - Ivan H. Dimovski

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Résumé :
1. Convolutions of Linear Operators. Multipliers and Multiplier Quotients.- 1.1. The Duhamel Convolution.- 1.2. The Mikusi?ski Ring.- 1.3. Convolutions of Linear Endomorphisms.- 1.4. The Multiplier Quotients Ring of an Annihilators-free Convolutional Algebra.- 2. Convolutions of General Integration Operators. Applications.- 2.1. Convolutions of the Linear Right Inverses of the Differentiation Operator.- 2.2. An Application of the Convolutional Approach to Dirichlet Expansions of Locally Holomorphic Functions.- 2.3. A Convolution for the General Right Inverse of the Backward Shift Operator in Spaces of Locally Holomorphic Functions.- 2.4. Convolutions and Commutants of the Gelfond-Leontiev Integration Operator and of Its Integer Powers.- 2.5. Operational Calculi for the Bernoulli Integration Operator.- 3. Convolutions Connected with Second-Order Linear Differential Operators.- 3.1. Convolutions of Right Inverse Operators of the Square of the Differentiation.- 3.2. Convolutions of Initial Value Right Inverses of Linear Second-Order Differential Operators.- 3.3. Convolutions of Boundary Value Right Inverses of Linear Second-Order Differential Operators.- 3.4. Applications of Convolutions to Non-Local Boundary Value Problems.- References.- Authors index....

Sommaire:
1. Convolutions of Linear Operators. Multipliers and Multiplier Quotients.- 1.1. The Duhamel Convolution.- 1.2. The Mikusi?ski Ring.- 1.3. Convolutions of Linear Endomorphisms.- 1.4. The Multiplier Quotients Ring of an Annihilators-free Convolutional Algebra.- 2. Convolutions of General Integration Operators. Applications.- 2.1. Convolutions of the Linear Right Inverses of the Differentiation Operator.- 2.2. An Application of the Convolutional Approach to Dirichlet Expansions of Locally Holomorphic Functions.- 2.3. A Convolution for the General Right Inverse of the Backward Shift Operator in Spaces of Locally Holomorphic Functions.- 2.4. Convolutions and Commutants of the Gelfond-Leontiev Integration Operator and of Its Integer Powers.- 2.5. Operational Calculi for the Bernoulli Integration Operator.- 3. Convolutions Connected with Second-Order Linear Differential Operators.- 3.1. Convolutions of Right Inverse Operators of the Square of the Differentiation.- 3.2. Convolutions of Initial Value Right Inverses of Linear Second-Order Differential Operators.- 3.3. Convolutions of Boundary Value Right Inverses of Linear Second-Order Differential Operators.- 3.4. Applications of Convolutions to Non-Local Boundary Value Problems.- References.- Authors index.