Convolutional Calculus

'Et moi, .... si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alIe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Texte du rabat

'Et moi, .... si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alIe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Contenu

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.