Factorization of matrix functions and singular integral operators Book

Book the First: "Of bodies chang'd to various forms, I sing" The world is a constant changes… Everything moves and one thing always changes into the other.
The earth was created by the god unknown as a sphere hanging in space… And life there was an idyll: no crimes, no enmity no wars… "From veins of vallies, milk and nectar broke; And honey sweating through the pores of oak."
But then the human history started and the deterioration began… "Truth, modesty, and shame, the world forsook: Fraud, avarice, and force, their places took."
Sins multiply and on observing the cases of cannibalism, Jove decides to destroy the sinful seed with the global deluge and to plant new generation of human beings sowing stones and turning them into males and females… "What the man threw, assum'd a manly face; And what the wife, renew'd the female race." And then the multiple, fantastic and fabulous metamorphoses of deities commenced…
Changes, alterations, transformations…

Book the Second: Now it's time for incompetent Phaeton to take his disastrous trip through the sky… "Th' astonisht youth, where-e'er his eyes cou'd turn, Beheld the universe around him burn…" And the corresponding place in the Bible: "Then the Lord rained upon Sodom and upon Gomorrah brimstone and fire from the Lord out of heaven…" Genesis 19:24. Both events are probably the references to the Minoan eruption of Thera, which was a major catastrophic volcanic eruption in recorded history.
Arrogant deities keep intriguing, fornicating and stealing shamelessly… They are ready to use any means… "Livid and meagre were her looks, her eye In foul distorted glances turn'd awry; A hoard of gall her inward parts possess'd, And spread a greenness o'er her canker'd breast; Her teeth were brown with rust, and from her tongue, In dangling drops, the stringy poison hung." This description of Envy is flowery and magnificent.
Deception and revenge are the way of Gods…

Book the Third: No one, except the major deities, is safe from a pernicious metamorphosis and fatal perishment. Transformations are miraculous and unpredictable: Actaeon into a stag; Tiresias into a woman; Narcissus into a flower; Echo into an incorporeal voice and mariners into dolphins…
The archetype of dragon seems to have been known since the most ancient times… And the sowing of the dragon's teeth have afterwards become the attribute of many fairytales: "He sows the teeth at Pallas's command, And flings the future people from his hand."
The story of Tiresias as an arbiter of male and female sexual pleasures is the most picturesque: "'The sense of pleasure in the male is far More dull and dead, than what you females share.' Juno the truth of what was said deny'd; Tiresias therefore must the cause decide, For he the pleasure of each sex had try'd."
Much earlier Tiresias appears in Homer's Odyssey as a prophetic ghost in the land of the dead.
In the last century Tiresias was mentioned in the progressive rock song The Cinema Show by Genesis: "Once a man, like the sea I raged, Once a woman, like the earth I gave."
The tale of Narcissus is an allegory of egocentrism and the story of Pentheus is a fable of the foolish obduracy.

Book the Fourth: An intrigue of The Story of Pyramus and Thisbe, especially in the end, reminds of that in Romeo and Juliet: "Then in his breast his shining sword he drown'd, And fell supine, extended on the ground. As out again the blade lie dying drew, Out spun the blood, and streaming upwards flew." Now it is clear where the inspiration came from.
"As when the stock and grafted twig combin'd Shoot up the same, and wear a common rind: Both bodies in a single body mix, A single body with a double sex." The image of Hermaphroditus was integrated both in poetry and in modern pop culture. "Where between sleep and life some brief space is, With love like gold bound round about the head, Sex to sweet sex with lips and limbs is wed, Turning the fruitful feud of hers and his To the waste wedlock of a sterile kiss…" Algernon Charles Swinburne - Hermaphroditus
"From a dense forest of tall dark pinewood, Mount Ida rises like an island. Within a hidden cave, nymphs had kept a child; Hermaphroditus, son of gods, so afraid of their love." Genesis - The Fountain of Salmacis
The gods have a rich imagination and a wry sense of humour so the miraculous changes they work on the others are unpredictable.

Book the Fifth: The description of the massacre at the feast is a pure satire… Who can be a match for Perseus possessing such a mighty weapon of mass destruction as Medusa's head?
"Weak was th' usurper, as his cause was wrong; Where Gorgon's head appears, what arms are strong? When Perseus to his host the monster held, They soon were statues, and their king expell'd."
Lewd Pyreneus decided to keep all the Muses in his private harem but they turned into birds and flew away while the unlucky libertine lacking creative imagination just fell from a tower: "Then, in a flying posture wildly plac'd, And daring from that height himself to cast, The wretch fell headlong, and the ground bestrew'd With broken bones, and stains of guilty blood."
And the tale of Ceres and Proserpine is one of the archetypal myths explaining the existence of seasons: "Jove some amends for Ceres lost to make, Yet willing Pluto shou'd the joy partake, Gives 'em of Proserpine an equal share, Who, claim'd by both, with both divides the year. The Goddess now in either empire sways, Six moons in Hell, and six with Ceres stays."

Book the Sixth: In the tales of Arachne and Niobe Ovid just ridicules the vainglory and smugness of gods and their unmotivated cruelty too: "Next she design'd Asteria's fabled rape, When Jove assum'd a soaring eagle's shape: And shew'd how Leda lay supinely press'd, Whilst the soft snowy swan sate hov'ring o'er her breast, How in a satyr's form the God beguil'd, When fair Antiope with twins he fill'd. Then, like Amphytrion, but a real Jove, In fair Alcmena's arms he cool'd his love." Arachne's tapestry is a set of sheer evidences against gods' lechery and she has obviously won but Goddess in fury destroyed the masterpiece and turned Arachne into a spider: "This the bright Goddess passionately mov'd, With envy saw, yet inwardly approv'd. The scene of heav'nly guilt with haste she tore, Nor longer the affront with patience bore; A boxen shuttle in her hand she took, And more than once Arachne's forehead struck."
And so it is with a coldblooded murder of Niobe's children.
The tale of Tereus, Procne and Philomela is something like a horror mystery told in the goriest hues: "But soon her tongue the girding pinchers strain, With anguish, soon she feels the piercing pain: Oh father! father! would fain have spoke, But the sharp torture her intention broke; In vain she tries, for now the blade has cut Her tongue sheer off, close to the trembling root."
This book is a very sanguinary one.

Book the Seventh: Medea knows her witchcraft: "In a large cauldron now the med'cine boils, Compounded of her late-collected spoils, Blending into the mesh the various pow'rs Of wonder-working juices, roots, and flow'rs; With gems i' th' eastern ocean's cell refin'd, And such as ebbing tides had left behind; To them the midnight's pearly dew she flings, A scretch-owl's carcase, and ill boding wings; Nor could the wizard wolf's warm entrails scape (That wolf who counterfeits a human shape)."
"Fillet of a fenny snake, In the cauldron boil and bake; Eye of newt and toe of frog, Wool of bat and tongue of dog, Adder's fork and blind-worm's sting, Lizard's leg and howlet's wing, For a charm of pow'rful trouble, Like a hell-broth boil and bubble." William Shakespeare - Macbeth
The methods of witches and their cooking recipes hardly changed since Ovid's time.
This book seems to be less impressive than the previous ones.

Book the Eighth: The greater part of the book is the tales of traitorous Scylla and hunting for the ferocious boar.
The most famous legends of Minotaur: "These private walls the Minotaur include, Who twice was glutted with Athenian blood: But the third tribute more successful prov'd, Slew the foul monster, and the plague remov'd. When Theseus, aided by the virgin's art, Had trac'd the guiding thread thro' ev'ry part, He took the gentle maid, that set him free, And, bound for Dias, cut the briny sea. There, quickly cloy'd, ungrateful, and unkind, Left his fair consort in the isle behind…" and Icarus: "When now the boy, whose childish thoughts aspire To loftier aims, and make him ramble high'r, Grown wild, and wanton, more embolden'd flies Far from his guide, and soars among the skies. The soft'ning wax, that felt a nearer sun, Dissolv'd apace, and soon began to run. The youth in vain his melting pinions shakes, His feathers gone, no longer air he takes: Oh! Father, father, as he strove to cry, Down to the sea he tumbled from on high, And found his Fate; yet still subsists by fame, Among those waters that retain his name." are told just en passant…
And the beautiful story of Philemon and Baucis is most warmhearted and even romantic.

Book the Ninth: Vicissitudes of love keep ruling over both gods and mortals…
I liked how an origin of cornucopia was described: "Nor yet his fury cool'd; 'twixt rage and scorn, From my maim'd front he tore the stubborn horn: This, heap'd with flow'rs, and fruits, the Naiads bear, Sacred to plenty, and the bounteous year."
And the process of turning of Heracles into a constellation was beautiful: "So when Alcides mortal mold resign'd, His better part enlarg'd, and grew refin'd; August his visage shone; almighty Jove In his swift carr his honour'd offspring drove; High o'er the hollow clouds the coursers fly, And lodge the hero in the starry sky."
I especially enjoyed the tale of Iphis and Ianthe. Even Egyptian goddess Isis had her finger in the pie - she assisted two girls in love with each other transforming one of them into a youth making thus their love legal: "Not much in fear, nor fully satisfy'd; But Iphis follow'd with a larger stride: The whiteness of her skin forsook her face; Her looks embolden'd with an awful grace; Her features, and her strength together grew, And her long hair to curling locks withdrew. Her sparkling eyes with manly vigour shone, Big was her voice, audacious was her tone. The latent parts, at length reveal'd, began To shoot, and spread, and burnish into man. The maid becomes a youth; no more delay Your vows, but look, and confidently pay."
All we need is love…

Book the Tenth: Story of Orpheus and Eurydice seems to be most popular in the world of poetry, arts, literature and even music. And "Never look back" is also an archetypal motif in myths, the Bible (Lot's wife) and many fairytales all over the world: "They well-nigh now had pass'd the bounds of night, And just approach'd the margin of the light, When he, mistrusting lest her steps might stray, And gladsome of the glympse of dawning day, His longing eyes, impatient, backward cast To catch a lover's look, but look'd his last; For, instant dying, she again descends, While he to empty air his arms extends."
Pygmalion carved his statue in ivory: "Yet fearing idleness, the nurse of ill, In sculpture exercis'd his happy skill; And carv'd in iv'ry such a maid, so fair, As Nature could not with his art compare…" so it couldn't be bigger than a figurine or a statuette but the story goes as if it were lifesize.
And the clinical case of Myrrha's incestual lust is told in a weird psychoanalytical style of Sigmund Freud.
And anemone is an extremely anemic flower: "Still here the Fate of lovely forms we see, So sudden fades the sweet Anemonie. The feeble stems, to stormy blasts a prey, Their sickly beauties droop, and pine away."

Book the Eleventh: Orpheus has met the bitter end - he was ripped to shreds by drunken Maenads: "His mangled limbs lay scatter'd all around, His head, and harp a better fortune found; In Hebrus' streams they gently roul'd along, And sooth'd the waters with a mournful song." Somehow, this reminded me of the mass hysteria of the Beatles' concerts in the middle of the sixties…
Ever since my childhood I was fascinated with the fable of King Midas - I enjoyed both his golden touch foolishness: "He pluck'd the corn, and strait his grasp appears Fill'd with a bending tuft of golden ears," and his award of ass's ears: "Fix'd on his noddle an unseemly pair, Flagging, and large, and full of whitish hair; Without a total change from what he was, Still in the man preserves the simple ass."
"Pan tun'd the pipe, and with his rural song Pleas'd the low taste of all the vulgar throng; Such songs a vulgar judgment mostly please, Midas was there, and Midas judg'd with these." It reads exactly as if Ovid portrayed the showbiz and music critics of today.
And Ceyx's hapless attempt at seafaring is in a way quite antithetical to The Odyssey: "An universal cry resounds aloud, The sailors run in heaps, a helpless crowd; Art fails, and courage falls, no succour near; As many waves, as many deaths appear." The sea always was a merciless widow-maker.

Book the Twelfth: This book is of war and warriors. One strangled warrior was turned into a swan and one raped maiden was turned into male warrior… The incessant descriptions of battles are too monotonous and tedious and even the death of Achilles seems to be unimpressive: "Of all the mighty man, the small remains
A little urn, and scarcely fill'd, contains."

Book the Thirteenth: Troy fell. Ajax and Ulysses compete for dead Achilles' magical armor. "Brawn without brain is thine: my prudent care Foresees, provides, administers the war…" Ulysses declares and wins… "Now cannot his unmaster'd grief sustain, But yields to rage, to madness, and disdain…" Unable to endure his dishonor, Ajax falls upon his own sword… War is evil… Make love, not war.

Book the Fourteenth: Nymphomaniac sorceress Circe embarks on a spree of malicious alterations: out of jealousy she turns Scylla into a bloodthirsty monster: "Soon as the nymph wades in, her nether parts Turn into dogs; then at her self she starts…" and she turns innocent sailors into beasts: "Soon, in a length of face, our head extends; Our chine stiff bristles bears, and forward bends: A breadth of brawn new burnishes our neck; Anon we grunt, as we begin to speak." And with many adventures Ulysses sails on and on…

Book the Fifteenth: Rome is founded and caesars begin to reign trying to usurp divine power of their gods…
"The work is finish'd, which nor dreads the rage Of tempests, fire, or war, or wasting age…"
Gods are like humans but they are more vainglorious, more powerful, more cunning, more perfidious, more libidinous and much more vengeful.