Thesis (Ph. D.)--Carleton University, 2001. / Includes bibliographical references (p. 118-133). Also available in electronic format on the Internet.

Using C. Fefferman's embedding of a charge space in a measure space allows us to apply standard interpolation theorems to the establishment of norm inequalities for Besicovitch almost periodic functions. This yields a significant improvement to the results of A. Avantaggiati, G. Bruno and R. Iannacci. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

Thesis--Copenhagen. / "Litteraturfortegnelse": p. [93]-94.

Thesis--Copenhagen. / "Litteraturfortegnelse": p. [93]-94.

In this paper the non density of AP, the set of almost periodic functions in the sense of Bohr, in the space S of almost periodic functions in the sense of Stepanov is proven.

Thesis (Ph.D.)--Ohio University, June, 2005. / Includes bibliographical references (p. 96-102)

Thesis (Ph.D.)--Ohio University, June, 2005. / Title from PDF t.p. Includes bibliographical references (p. 96-102)

This thesis consists of two papers, enumerated by Roman numerals. The main focus is on the spectral theory of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?n" />-Laplacians. Here, an <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?n" />-Laplacian, for integer <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?n" />, refers to a metric graph equipped with a differential operator whose differential expression is the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?2n" />-th derivative. In Paper I, a classification of all vertex conditions corresponding to self-adjoint <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?n" />-Laplacians is given, and for these operators, a secular equation is derived. Their spectral asymptotics are analysed using the fact that the secular function is close to a trigonometric polynomial, a type of almost periodic function. The notion of the quasispectrum for <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?n" />-Laplacians is introduced, identified with the positive roots of the associated trigonometric polynomial, and is proved to be unique. New results about almost periodic functions are proved, and using these it is shown that the quasispectrum asymptotically approximates the spectrum, counting multiplicities, and results about asymptotic isospectrality are deduced. The results obtained on almost periodic functions have wider applications outside the theory of differential operators. Paper II deals more specifically with bi-Laplacians (<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?n=2" />), and a notion of standard conditions is introduced. Upper and lower estimates for the spectral gap --- the difference between the two lowest eigenvalues - for these standard conditions are derived. This is achieved by adapting the methods of graph surgery used for quantum graphs to fourth order differential operators. It is observed that these methods offer stronger estimates for certain classes of metric graphs. A geometric version of the Ambartsumian theorem for these operators is proved.

Neste trabalho estudaremos a existência de soluções fracas, pseudo quase periódicas e periódicas, para uma classe de sistemas não autônomo do tipo neutro com retardamento não limitado modelados na forma \' d SUP. dt\' (u(t) + F(t, ut)) = A(t)u(t) + G(t, \'u IND.t\' ), t \'PERTENCE A\' (0, a), \'u IND. 0\' = \'varphi\' \'PERTENCE A\' B, onde {A(t)} ´e uma família de operadores lineares fechados, com um dom´?nio comum D =D(A(t)), a história ut : (-\'INFINITO\'1, 0] \'SETA\' X, \'u IND. t\'(THETA) = u(t+\'THETA\'), pertence a um espaço de fase abstrato B definido axiomaticamente e F,G : [0, a] × B \'SETA\' X são funções apropriadas. Para obter alguns de nossos resultados, precisaremos usar as propriedades da família de operadores de evolução (U(t, s))\'t > OU=\'s, para o sistema u? (t) - A(t)u(t) = 0, t \'Pertencer A\' (0, a), \'u IND.0\' = \'phi\', onde U(t, s) ´e uma fam´?lia de operadores lineares limitados em X / In this work we study the existence of mild, pseudo almost-periodic and periodic solution, concepts introduced be later for a class of abstract neutral functional systems with unbounded delay in the form \'d SUP dt\' (u(t) + F(t, \'u IND.t\')) = A(t)u(t) + G(t, \'u IND. t\'), t IT BELONGS\' (0, a), \'u IND.0\' = \'varphi\' \'IT BELONGS\' , where is a family of closed linear operator in a Banach space X, with a common domain D = D(A(t)), t \'IT BELONGS\' R, densely defined in X; the history \'u IND. t\' : (-\'THE infinite\', 0] \' ARROW\' X, ut(\'THETA\') = x(t+\'THETA\'), belongs to some abstract phase space B defined axiomatically and F,G : I ×B \'ARROW\' X are appropriate functions and I is a bounded or unbounded interval in R. To establish some of our results, we will use the properties of a systems of evolution (U(t, s))\' t IND. > OR =\'s, for a system in the form u? (t) - A(t)u(t) = 0, t \'IT BELONGS\' (0, a), \'u IND.0\' = \'PHI\', where (U(t, s))\'t IND. > 0R =\'s is a family of bounded linear operators on X

Neste trabalho estudaremos a existência de soluções fracas, pseudo quase periódicas e periódicas, para uma classe de sistemas não autônomo do tipo neutro com retardamento não limitado modelados na forma \' d SUP. dt\' (u(t) + F(t, ut)) = A(t)u(t) + G(t, \'u IND.t\' ), t \'PERTENCE A\' (0, a), \'u IND. 0\' = \'varphi\' \'PERTENCE A\' B, onde {A(t)} ´e uma família de operadores lineares fechados, com um dom´?nio comum D =D(A(t)), a história ut : (-\'INFINITO\'1, 0] \'SETA\' X, \'u IND. t\'(THETA) = u(t+\'THETA\'), pertence a um espaço de fase abstrato B definido axiomaticamente e F,G : [0, a] × B \'SETA\' X são funções apropriadas. Para obter alguns de nossos resultados, precisaremos usar as propriedades da família de operadores de evolução (U(t, s))\'t > OU=\'s, para o sistema u? (t) - A(t)u(t) = 0, t \'Pertencer A\' (0, a), \'u IND.0\' = \'phi\', onde U(t, s) ´e uma fam´?lia de operadores lineares limitados em X / In this work we study the existence of mild, pseudo almost-periodic and periodic solution, concepts introduced be later for a class of abstract neutral functional systems with unbounded delay in the form \'d SUP dt\' (u(t) + F(t, \'u IND.t\')) = A(t)u(t) + G(t, \'u IND. t\'), t IT BELONGS\' (0, a), \'u IND.0\' = \'varphi\' \'IT BELONGS\' , where is a family of closed linear operator in a Banach space X, with a common domain D = D(A(t)), t \'IT BELONGS\' R, densely defined in X; the history \'u IND. t\' : (-\'THE infinite\', 0] \' ARROW\' X, ut(\'THETA\') = x(t+\'THETA\'), belongs to some abstract phase space B defined axiomatically and F,G : I ×B \'ARROW\' X are appropriate functions and I is a bounded or unbounded interval in R. To establish some of our results, we will use the properties of a systems of evolution (U(t, s))\' t IND. > OR =\'s, for a system in the form u? (t) - A(t)u(t) = 0, t \'IT BELONGS\' (0, a), \'u IND.0\' = \'PHI\', where (U(t, s))\'t IND. > 0R =\'s is a family of bounded linear operators on X