Reports of cases adjudged in the Court of Chancery of New-York, containing the cases from March, 1814 to [July, 1823] ... inclusive.

"Appendix. Sketch of the life and character of John Wells, esquire:" p. [331]-343 at end v. 7.

The minstrel of the North; or, Cumbrian legends; being a poetical miscellany of legendary, Gothic and romantic, tales.

Mode of access: Internet.

The ancient history of the Egyptians, Carthaginians, Assyrians, Babylonians, Medes & Persians, Macedonians, and Grecians /

Vol. 1: xi, [2], 14-319, [1] p., [1] folded leaf of plates (last page blank); v. 2: iv, [1], 6-302 p.; v. 3: iv, [1], 6-312 p.; v. 4: 287, [1] p. (last page blank); v. 5: iv, [1], 6-323, [1] p. (last page blank); v. 6: iv, [1], 6-302 p.; v. 7: iv, [1], 6-326 p.; v. 8: iv, [1], 6-296 p.; v. 9: iv, [1], 6-311, [1] p. (last page blank); v. 10: [4], 250 p.

The Missionary pioneer, or, A brief memoir of the life, labours, and death of John Stewart, (man of colour) founder, under God of the mission among the Wyandotts at Upper Sandusky, Ohio / Published by Joseph Mitchell.

http://www.archive.org/details/missionarypionee00stewrich

Biographical sketches of General Nathaniel Massie, General Duncan McArthur, Captain William Wells, and General Simon Kenton: who were early settlers in the western country.

Mode of access: Internet.

A book of miscellanies, 1770

A legal commonplace book by kept by Henry Wells of Worcester, Mass. Focuses on such topics as libel of a man to his wife, common recovery in writs and deeds, pleadings, trover, damages and costs, imprisonment, leases, mortgages, covenants, and ejectment. Also contains a number of miscellaneous entries touching on abridgements of law texts, minutes of court proceedings, kings of England, and biblical quotes. Five-page index located at the end of the work.

Memoirs of Mr. John Tobin ...

Preface,--Memoirs of Mr. John Tobin.--Analysis, by John Tobin, of La gitanilla de Madrid, Comedia famosa de Don Antonio de Solis.--The tragedy, a fragment.--The Indians, a play.--Your's or mine, a comic opera.--The fisherman, an opera.

The life and correspondence of John Foster:

Mode of access: Internet.

The life and correspondence of John Foster:

v. 1 has imprint: London, Bohn, 1861.

The missionary pioneer : or, a brief memoir of the life, labours, and death of John Stewart, (man of colour) founder, under God, of the mission among the Wyandotts at Upper Sandusky, Ohio /

Reprint of: New York : J.C. Totten, 1827.

Wells' Every man his own lawyer and United States form book : being a complete guide in all matters of law and business negotiations, for every state in the Union ...

Mode of access: Internet.

The missionary pioneer : or, A brief memoir of the life, labours, and death of John Stewart, (man of colour,) founder, under God, of the mission among the Wyandotts, at Upper Sandusky, Ohio, /

Photocopy. Ann Arbor, Mich. : University Microfilms International, 1980.--21 cm.

Smooth Banach spaces and approximations

If E and F are real Banach spaces let C^p,q(E, F) O ≤ q ≤ p ≤ ∞, denote those maps from E to F which have p continuous Frechet derivatives of which the first q derivatives are bounded. A Banach space E is defined to be C^p,q smooth if C^p,q(E,R) contains a nonzero function with bounded support. This generalizes the standard C^p smoothness classification.

If an L^p space, p ≥ 1, is C^q smooth then it is also C^q,q smooth so that in particular L^p for p an even integer is C^∞,∞ smooth and L^p for p an odd integer is C^p-1,p-1 smooth. In general, however, a C^p smooth B-space need not be C^p,p smooth. C_o is shown to be a non-C^2,2 smooth B-space although it is known to be C^∞ smooth. It is proved that if E is C^p,1 smooth then C_o(E) is C^p,1 smooth and if E has an equivalent C^p norm then c_o(E) has an equivalent C^p norm.

Various consequences of C^p,q smoothness are studied. If f ϵ C^p,q(E,F), if F is C^p,q smooth and if E is non-C^p,q smooth, then the image under f of the boundary of any bounded open subset U of E is dense in the image of U. If E is separable then E is C^p,q smooth if and only if E admits C^p,q partitions of unity; E is C^p,psmooth, p ˂∞, if and only if every closed subset of E is the zero set of some C^P function.

f ϵ C^q(E,F), 0 ≤ q ≤ p ≤ ∞, is said to be C_p,q approximable on a subset U of E if for any ϵ ˃ 0 there exists a g ϵ C^p(E,F) satisfying

sup/xϵU, O≤k≤q ‖ D^k f(x) - D^k g(x) ‖ ≤ ϵ.

It is shown that if E is separable and C^p,q smooth and if f ϵ C^q(E,F) is C_p,q approximable on some neighborhood of every point of E, then F is C_p,q approximable on all of E.

In general it is unknown whether an arbitrary function in C¹(l², R) is C_2,1 approximable and an example of a function in C¹(l², R) which may not be C_2,1 approximable is given. A weak form of C_∞,q, q≥1, to functions in C^q(l², R) is proved: Let {U_α} be a locally finite cover of l² and let {T_α} be a corresponding collection of Hilbert-Schmidt operators on l². Then for any f ϵ C^q(l²,F) such that for all α

sup ‖ D^k(f(x)-g(x))[T_αh]‖ ≤ 1.

xϵU_α,‖h‖≤1, 0≤k≤q